title: Mandalay Bay

text: In January 2020, Mandalay Bay was named the pre- and post-game venue for the Las Vegas Raiders, a football team which plays at the Allegiant Stadium directly west of the resort. That month, MGM Resorts also announced that it would sell Mandalay Bay to a joint venture consisting of MGM Growth Properties and The Blackstone Group. MGM would own 50.1 percent of the joint venture, and Blackstone would own the remainder. Mandalay Bay would be leased to MGM Resorts, which would continue to operate the resort. The deal was finalized in February 2020. Vici Properties acquired Mandalay Bay in April 2022, as part of its buyout of MGM Growth. In 2023, Vici plans to finalize a deal to buy out Blackstone's ownership stake in the resort.


title: Mandalay Bay

text: On October 1, 2017, gunman Stephen Paddock opened fire from his room on the hotel's 32nd floor. He targeted concertgoers attending a music festival, located diagonally across from the resort. He killed 60 people and wounded 867 others, before killing himself as authorities approached his room. The incident is the deadliest mass shooting by a lone gunman in U.S. history.


title: Mandalay Bay

text: Mandalay Bay remained open following the shooting. Hospitality experts believed the massacre would have only a minimal impact on the resort's revenue. Several hundred workers, out of 7,400, were laid off as a result of decreased visitation due to the shooting. MGM had also paused its marketing of the resort after the incident, which contributed to profit losses. Finances gradually improved, with a near-full recovery in 2019.


title: Mandalay Bay

text: Resort security was increased as a result of the shooting, while MGM announced that it had no plans to rent Paddock's suite out to future guests. Floors 31 through 34 were renumbered as 56 through 59. Numerous lawsuits were filed against MGM by the shooting survivors, alleging inadequate preventative measures at Mandalay Bay. The company and plaintiffs eventually settled for $800 million.


title: Mandalay Bay

text: The Mandalay Bay complex occupies 120 acres. The resort includes a casino. It initially opened with of gaming space, featuring 122 table games and 2,400 slot machines. As of 2006, the casino had one of the largest sports books in Las Vegas, with a wall of 31 television screens. The casino floor was renovated in 2013, with new carpeting and chairs added. The sports book was updated in 2018.


title: Mandalay Bay

text: Mandalay Bay has a tropical South Seas theme. Water features, including numerous fountains, are present throughout the resort. The hotel lobby features a two-story aquarium containing 12,600 gallons of water. The resort also has an aquatic attraction known as Shark Reef, which includes a aquarium. The $40 million facility opened on June 20, 2000, and contains the largest aquarium on the Strip, featuring mostly sharks.


title: Mandalay Bay

text: The 12,000-seat Mandalay Bay Events Center opened on April 10, 1999, and was renamed the Michelob Ultra Arena in 2021. It has hosted numerous entertainers as well as sports games.


title: Mandalay Bay

text: Construction on another facility, the Mandalay Bay Convention Center, began in 2001. Work was temporarily stopped due to the economic impact of the September 11 attacks. It eventually opened in January 2003, and is among the largest convention centers in the U.S. Convention business makes up a significant portion of the resort's revenue.


title: Mandalay Bay

text: When it opened, the resort included the Treasures of Mandalay Bay Museum, which had a rare currencies exhibit worth more than $40 million. Exhibit items included two $100,000 bills, among only a handful known to still exist.


title: Mandalay Bay

text: The Luxor and Excalibur resorts, also built by Mandalay Resort Group, are located north of Mandalay Bay. The term "Mandalay Mile" was created by company president Glenn Schaeffer in reference to the three resorts, which are connected via the Mandalay Bay Tram.


title: Mandalay Bay

text: In addition to Mandalay Bay's primary hotel, the property also includes two others: Delano Las Vegas (formerly THEhotel) and a Four Seasons hotel. Four Seasons shares a tower with Mandalay Bay, and Delano is operated in a second tower.


title: Mandalay Bay

text: Mandalay Bay has 3,209 rooms, excluding the other on-site hotels. The Mandalay Bay tower is built out in a Y-shaped layout. Rows of gold neon tubing run up the tower's sides, in between mirrored, gold-colored windows. Although the tower is 43 stories, the top four floors are numbered 60 through 63. Four Seasons occupies the 35th through 39th floors. The 40th through 42nd floors contain suites which are managed by Mandalay Bay. A club known as the Foundation Room operates on the top floor.


title: Mandalay Bay

text: Delano Las Vegas originally opened in December 2003, as THEhotel at Mandalay Bay. It was renamed in 2014. Like the Mandalay Bay tower, Delano is also 43 stories. It has 1,117 rooms, all of them suites. It is marketed as a separate hotel.


title: Mandalay Bay

text: The Mandalay Bay hotel rooms were upgraded in 2006, after MGM acquired the resort. A $100 million renovation of the rooms took place from 2015 to 2016.


title: Mandalay Bay

text: In June 1996, Circus Circus Enterprises announced its partnership with Four Seasons Hotels, which would manage a hotel connected to Mandalay Bay. The Four Seasons hotel opened along with the resort on March 2, 1999. It marks the first Las Vegas location for Four Seasons Hotels, a luxury hotel company which, for years, had wanted to open a property in the area. The Four Seasons was built to compete with a growing number of upscale Strip resorts such as Bellagio.


title: Mandalay Bay

text: The Four Seasons includes 424 rooms, and has various amenities – including restaurants, lounges, a spa, and a health club – which are located in a two-story facility on the south side of the Mandalay Bay property. Most of the amenities at the Four Seasons are inaccessible to guests of Mandalay Bay. The hotel excludes gaming, although Mandalay Bay's casino and other amenities are open to guests of the Four Seasons.


title: Mandalay Bay

text: The Four Seasons has been favorably received by guests. Since 1999, it has been a repeat winner of the AAA Five Diamond Award. It was the first hotel in the Las Vegas Valley to win the award, and in 2000, it became the first in the area to add a permanent kosher kitchen. A renovation of the hotel concluded in December 2012.


title: Mandalay Bay

text: Mandalay Bay originally had 15 restaurants, 11 of which were leased out. Most of the restaurants opened with the resort, while three others debuted later in 1999.


title: Mandalay Bay

text: Among the restaurants is Aureole by chef Charlie Palmer, named after another restaurant of his in Manhattan. The Las Vegas Aureole was designed by Adam Tihany and includes a four-story wine tower made of glass and steel. It can hold 10,000 wine bottles, which are retrieved by harnessed workers. The tower is surrounded by stairs descending into the restaurant.


title: Mandalay Bay

text: Mandalay Bay also includes Trattoria del Lupo, the first Italian restaurant by chef Wolfgang Puck. Other celebrity chefs include Mary Sue Milliken and Susan Feniger, who opened Border Grill. A Russian-themed restaurant, Red Square, featured a 16-foot headless statue of Vladimir Lenin at its entrance. It also included a walk-in vodka freezer with a bar top made of ice.


title: Mandalay Bay

text: The resort also featured several Asian restaurants, including The Noodle Shop, and Shanghai Lily. The latter was designed by Tony Chi, and eventually closed in 2011. The entrance to another restaurant, China Grill, featured a moat and working drawbridge, which could be lifted to provide privacy for reserved parties. The adjacent China Grill Cafe and Zen Sum served dim sum on a conveyor belt counter, while robot carts with camera sensors brought food to diners elsewhere in the restaurant.


title: Mandalay Bay

text: By 2001, a new fine dining restaurant had opened as "3950", named after the resort's address. It served steaks and seafood, and included a lounge area with live cam footage of the Shark Reef. The restaurant was designed and managed by Mandalay Bay, unlike most of the others at the resort.


title: Mandalay Bay

text: Chef Hubert Keller opened Fleur de Lys, a French restaurant, in 2004. It operated for six years, before being remodeled and renamed as simply Fleur. In 2011, the restaurant began offering a $5,000 burger, which included a bottle of Petrus wine. Chef Fleur eventually departed Mandalay Bay in 2021, and the resort took over ownership and operations of his restaurant.


title: Mandalay Bay

text: As of 2006, Mandalay Bay had 23 restaurants. That year, chef Michael Mina opened his first steakhouse there, StripSteak. It also serves seafood, and includes a 70-seat bar and lounge area, serving more than 600 types of wine and more than 100 Scotch malts. Numerous restaurants were added in 2013, as part of ongoing renovations. Two decades after Mandalay Bay's opening, four of its original restaurants remained in operation, including Aureole, Lupo, and Border Grill. Red Square closed later that year, and was eventually replaced by the S Bar.


title: Mandalay Bay

text: Rumjungle, a restaurant and dance club, opened with the resort. The three-story Rumjungle included the world's largest rum bar and offered more than 100 varieties of rum. Guests would enter through an opening in a wall of flames. Rumjungle, which leased its space from the resort, filed for Chapter 11 bankruptcy in March 2010, to prevent its eviction. It alleged that Mandalay Bay broke its contract agreement, which stated that Rumjungle would be the sole nightclub at the resort; in 2008, Mandalay Bay opened a lounge venue known as "eyecandy", and Rumjungle stated that its profits suffered since then. The resort countered that Rumjungle's financial problems were due to the latter's outdated facilities and the Great Recession. Mandalay Bay eventually prevailed in litigation and evicted Rumjungle in August 2010. A new nightclub, Light, opened in its in place in 2013, in partnership with The Light Group and Cirque du Soleil.


title: Mandalay Bay

text: Mandalay Bay opened with a House of Blues music venue and restaurant, marking the chain's seventh location. The two-story House of Blues includes capacity for 1,800 people during concerts. It also has a retail store. The Las Vegas House of Blues would compete against the Hard Rock Hotel, which was known for hosting rock performances at its Joint venue. House of Blues had wanted to open a Las Vegas location for years, and partnered with Mandalay Bay after discussions with the Las Vegas Hilton failed to produce an agreement. The venue has hosted numerous entertainers, including Carlos Santana, who began a residency in 2012. He has performed there for more than a decade, and extended his residency to May 2026. Two live albums were also recorded there: "" by Yes (2000), and "Live in Las Vegas" by Macy Gray (2005).


title: Mandalay Bay

text: House of Blues also operates the Foundation Room, an upscale private bar and dining club on the hotel's top floor. It targets wealthy individuals, such as casino VIPs, corporate executives, and celebrities. Club membership is acquired through annual dues. In 2014, MGM agreed to pay a $500,000 fine after undercover police officers, during a sting operation, were provided with drugs and prostitutes at the Foundation Room by its employees. In 2020, the club removed a statue depicting Mahavira of the Jainism religion. Religious leaders had objected to the statue, calling its presence in a casino club inappropriate and disrespectful.


title: Mandalay Bay

text: Mandalay Bay includes a mall known as The Shoppes at Mandalay Place. The resort initially had 13 retail shops upon opening, with a full shopping mall planned for property between Mandalay Bay and the Luxor. Circus Circus Enterprises partnered with Westcor to develop the mall, and Nordstrom was announced as an anchor tenant in May 1999, with the mall's opening scheduled for 2001. However, the project was set back after Westcor dropped out later in 1999, unable to secure a second anchor tenant. Construction stopped in 2000, after Nordstrom also backed out. In May 2002, Mandalay Resort Group announced that it would resume construction, with the mall scaled back from to .


title: Mandalay Bay

text: Mandalay Place eventually opened in October 2003. It included 41 retailers, located along a 310-foot skybridge connecting Mandalay Bay to the Luxor. It opened with several retailers not found elsewhere in Las Vegas, in an effort to attract locals as well as tourists. Tenants have also comprised several restaurants, including two by chef Rick Moonen.


title: Mandalay Bay

text: Among the mall's notable retailers was the Reading Room, a bookstore popular for its author signings. The store was devised by Schaeffer, although the concept of a bookstore on the Strip was met with some skepticism. Schaeffer said, "What could be a more obvious place for a bookstore than a destination that has nearly 40 million visitors a year?" It was the only bookstore on the Strip until its closing in 2009.


title: Mandalay Bay

text: Ivan Kane's Forty Deuce, a speakeasy with burlesque 1940s-style dancers, operated at Mandalay Place from 2004 to 2009. 1923 Bourbon & Burlesque opened in its place in 2014, serving as a cigar lounge with a Prohibition era theme. Its primary attraction consisted of performances by Holly Madison and a burlesque troupe. Because of a dispute with her business partners, Madison departed 1923 Bourbon & Burlesque later in 2014, and it was renamed 1923 Prohibition Bar.


title: Mandalay Bay

text: The resort includes an 11-acre pool area known as Mandalay Bay Beach, which features 2,700 tons of sand imported from California. One of the pools includes a wave machine producing six-foot waves. It was designed to host championship surfing. The pool area also features a lazy river, and includes a stage for summer concerts, a stable since the resort's opening. This popularized the concept of poolside concerts at Las Vegas resorts.


title: Mandalay Bay

text: A topless sunbathing area known as Moorea Beach Club opened in 2003. It is named after Mo'orea, an island near Tahiti. The resort's pool area became popular among local families following the closure of the Wet 'n Wild water park in 2004. In 2013, The Light Group took over a area of the pool space and converted it into a dayclub and nightclub, known as Daylight Beach Club and Eclipse respectively.


title: Mandalay Bay

text: The resort includes the 1,800-seat Michael Jackson: One Theatre, originally known as the Mandalay Bay Theatre. Among Las Vegas tourists, entertainment offerings became increasingly popular during the 1990s, in addition to gambling. Circus Circus Enterprises believed that Las Vegas had evolved enough to support a full-time Broadway show. A production of the classic Broadway musical "Chicago" debuted at Mandalay Bay's 1999 grand opening and ran for one year. "Storm", an original production show featuring Latin music, weather effects, and aerialists, ran from April 2001 to July 2002.


title: Mandalay Bay

text: Both "Chicago" and "Storm" failed to achieve wide success. Schaeffer acknowledged that the resort needed "a more forceful and exciting show", prompting the addition of the Broadway musical "Mamma Mia!" in February 2003. It had a successful run which ended in January 2009, after approximately 2,300 performances. It was replaced by another Broadway show, Disney's "The Lion King", which ran from May 2009 to December 2011.


title: Mandalay Bay

text: During that time, resort executives realized that the property needed an A-list show, as many guests would travel elsewhere to see live entertainment. In response, Mandalay Bay partnered with Cirque du Soleil to create "", which eventually opened in May 2013. It is a music production show featuring numerous songs by late singer Michael Jackson.


title: Mandalay Bay

text: Mandalay Bay made its film debut in the 1999 film "Play It to the Bone", which shot in several areas of the resort. The first season of "Las Vegas" (2003) was also filmed partially at Mandalay Bay, which stood in as the fictional Montecito resort. Filming included the casino, lobby, and wave pool. A 2014 episode of "Modern Family", titled "Las Vegas", was also filmed at Mandalay Bay.


title: The Office (American season 6)

text: The sixth season of the American television comedy "The Office" premiered in the United States on NBC on September 17, 2009, and concluded on May 20, 2010. The season consisted of 22 half-hour episodes, and 2 hour-long episodes to comprise the 26 total episodes of material created. "The Office" is an American adaptation of the British TV series of the same name, and is presented in a mockumentary format, portraying the daily lives of office employees in the Scranton, Pennsylvania branch of the fictitious Dunder Mifflin Paper Company. The season stars Steve Carell, Rainn Wilson, John Krasinski, Jenna Fischer, B. J. Novak, and Ed Helms, with supporting performances from Leslie David Baker, Brian Baumgartner, Creed Bratton, Kate Flannery, Mindy Kaling, Ellie Kemper, Angela Kinsey, Paul Lieberstein, Oscar Nunez, Craig Robinson, and Phyllis Smith.


title: The Office (American season 6)

text: The season has been cited by several critics as weaker than earlier seasons, despite still receiving generally favorable reviews. The season ranked fifty-second in the season ratings with an average of 7.80 million viewers per episode, marking a steep drop in the ratings from the previous season which had an average of nine million viewers.


title: The Office (American season 6)

text: The sixth season of "The Office" aired on Thursdays at 9:00 p.m. (Eastern) in the United States. The season was released on DVD by Universal Studios Home Entertainment in a four-disc box set in the Region 1 area on September 7, 2010. The DVD set contains all 26 episodes, as well as commentaries from creators, writers, actors, and directors on some of the episodes. It also contains deleted scenes from all of the episodes, as well as bloopers.


title: The Office (American season 6)

text: The sixth season of the show was produced by Reveille Productions and Deedle-Dee Productions, both in association with Universal Media Studios. The show is based upon the British series created by Ricky Gervais and Stephen Merchant, both of whom are executive producers on both the US and UK versions. "The Office" is produced by Greg Daniels, who is also an executive producer. Daniels would have a limited role in this season, only co-writing an episode and directing another, as he was busy writing his new show, "Parks and Recreation" which he co-created with "Office" writer/producer Michael Schur, who left the writing staff of "The Office" after season four to focus on the new show. Returning writers from the previous season include Mindy Kaling, B. J. Novak, Paul Lieberstein, Lee Eisenberg, Gene Stupnitsky, Brent Forrester, Justin Spitzer, Jennifer Celotta, Aaron Shure, Charlie Grandy, Warren Lieberstein, and Halsted Sullivan. New writers in the sixth season include Daniel Chun, Jason Kessler (who served as script coordinator) and Jonathan Hughes (who previously wrote several of the "Office" webisodes). Lieberstein served as executive producer and showrunner. Kaling, Novak, Eisenberg, Stupnitsky and Shure were co-executive producers; Celotta and Forrester were consulting producers; Chun was a supervising producer; and Spitzer, Grandy, Warren Lieberstein and Halsted Sullivan were producers.


title: The Office (American season 6)

text: This season featured 26 episodes directed by 20 directors. Paul Lieberstein, Randall Einhorn and Seth Gordon each directed several episodes during the season. Writers Jennifer Celotta, Lee Eisenberg and Brent Forrester each directed episodes. Cast members B. J. Novak, John Krasinski, Steve Carell, Mindy Kaling and Rainn Wilson all directed episodes as well.


title: The Office (American season 6)

text: Many characters portrayed by "The Office" cast are based on the British version of the show. While these characters normally have the same attitude and perceptions as their British counterparts, the roles have been redesigned to better fit the American show. The show is known for its generally large cast size, with many of its actors and actresses known particularly for their improvisational work.


title: The Office (American season 6)

text: The sixth-season premiere "Gossip" received a 4.0 share in the Nielsen ratings among viewers aged 18 to 49, meaning that 4.0% of viewers aged 18 to 49 watched the episode. The episode was seen by 8.21 million viewers. The show ranked 17th in the seasonal 18–49 demographic ratings with an average of a 4.0 rating in the demographic. The viewership was an 18 percent drop compared to the fifth-season premiere, "Weight Loss". The season finale, "Whistleblower" was viewed by 6.60 million viewers with a 3.4 rating/10% share in the 18–49, marking a 3% drop from the fifth-season finale, "Company Picnic." The season also ranked 52nd in the seasonal total viewership with an average of 7.80 million viewers.


title: The Office (American season 6)

text: The sixth season received generally favorable reviews, with an overall score of 78/100 on Metacritic. However, some critics identified a decline in quality compared to previous seasons. The season mainly faced criticism for a lack of stakes for the characters. Some critics have also criticized the conclusion to the Jim and Pam romance while others were critical of the lack of growth for Michael. Cindy White of IGN gave the season a 7.5 saying it was "Good" and "We did get some funny moments and some good episodes in Season 6, but as a whole it just doesn't compare to the strength of seasons past." She also went on to criticize the storylines including Jim's stint as co-manager. Will Leitch of "New York" said ""The Office"'s season six was usually funny and always big-hearted, but there was never much at stake". "Entertainment Weekly" writer Darren Franich called the season the "least cohesive" season of the series.


title: The Office (American season 6)

text: The show received numerous nominations. The show was nominated for Favorite TV Comedy at the 36th People's Choice Awards, but lost to "The Big Bang Theory". The show was nominated for Screen Actors Guild Award for Outstanding Performance by an Ensemble in a Comedy Series for the fourth time at the 16th Screen Actors Guild Awards, but lost to "Glee". It was also nominated for two awards at Writers Guild of America Awards 2009 for Comedy Series and Episodic Comedy for the episode "Gossip" written by Paul Lieberstein. This season received four Emmy nominations at the 62nd Primetime Emmy Awards—Outstanding Comedy Series, Outstanding Lead Actor in a Comedy Series (Steve Carell), Outstanding Writing for a Comedy Series (Greg Daniels and Mindy Kaling for "Niagara") and Outstanding Sound Mixing for a Comedy or Drama Series (Half-Hour) and Animation.


title: The Office (American season 6)

text: In the following table, "U.S. viewers (million)" refers to the number of Americans who viewed the episode on the night of broadcast. Episodes are listed by the order in which they aired, and may not necessarily correspond to their production codes.


title: Context-free grammar

text: In formal language theory, a context-free grammar (CFG) is a formal grammar whose production rules are of the form


title: Context-free grammar

text: with formula_2 a "single" nonterminal symbol, and formula_3 a string of terminals and/or nonterminals (formula_3 can be empty). A formal grammar is "context-free" if its production rules can be applied regardless of the context of a nonterminal. No matter which symbols surround it, the single nonterminal on the left hand side can always be replaced by the right hand side. This is what distinguishes it from a context-sensitive grammar.


title: Context-free grammar

text: A formal grammar is essentially a set of production rules that describe all possible strings in a given formal language. Production rules are simple replacements. For example, the first rule in the picture,


title: Context-free grammar

text: replaces formula_6 with formula_7. There can be multiple replacement rules for a given nonterminal symbol. The language generated by a grammar is the set of all strings of terminal symbols that can be derived, by repeated rule applications, from some particular nonterminal symbol ("start symbol").


title: Context-free grammar

text: Nonterminal symbols are used during the derivation process, but do not appear in its final result string.


title: Context-free grammar

text: Languages generated by context-free grammars are known as context-free languages (CFL). Different context-free grammars can generate the same context-free language. It is important to distinguish the properties of the language (intrinsic properties) from the properties of a particular grammar (extrinsic properties). The language equality question (do two given context-free grammars generate the same language?) is undecidable.


title: Context-free grammar

text: Context-free grammars arise in linguistics where they are used to describe the structure of sentences and words in a natural language, and they were invented by the linguist Noam Chomsky for this purpose. By contrast, in computer science, as the use of recursively-defined concepts increased, they were used more and more. In an early application, grammars are used to describe the structure of programming languages. In a newer application, they are used in an essential part of the Extensible Markup Language (XML) called the "Document Type Definition".


title: Context-free grammar

text: In linguistics, some authors use the term phrase structure grammar to refer to context-free grammars, whereby phrase-structure grammars are distinct from dependency grammars. In computer science, a popular notation for context-free grammars is Backus–Naur form, or "BNF".


title: Context-free grammar

text: Since the time of Pāṇini, at least, linguists have described the grammars of languages in terms of their block structure, and described how sentences are recursively built up from smaller phrases, and eventually individual words or word elements. An essential property of these block structures is that logical units never overlap. For example, the sentence:


title: Context-free grammar

text: A context-free grammar provides a simple and mathematically precise mechanism for describing the methods by which phrases in some natural language are built from smaller blocks, capturing the "block structure" of sentences in a natural way. Its simplicity makes the formalism amenable to rigorous mathematical study. Important features of natural language syntax such as agreement and reference are not part of the context-free grammar, but the basic recursive structure of sentences, the way in which clauses nest inside other clauses, and the way in which lists of adjectives and adverbs are swallowed by nouns and verbs, is described exactly.


title: Context-free grammar

text: Context-free grammars are a special form of Semi-Thue systems that in their general form date back to the work of Axel Thue.


title: Context-free grammar

text: The formalism of context-free grammars was developed in the mid-1950s by Noam Chomsky, and also their classification as a special type of formal grammar (which he called phrase-structure grammars). Some authors, however, reserve the term for more restricted grammars in the Chomsky hierarchy: context-sensitive grammars or context-free grammars. In a broader sense, phrase structure grammars are also known as constituency grammars. The defining trait of phrase structure grammars is thus their adherence to the constituency relation, as opposed to the dependency relation of dependency grammars. In Chomsky's generative grammar framework, the syntax of natural language was described by context-free rules combined with transformation rules.


title: Context-free grammar

text: Block structure was introduced into computer programming languages by the Algol project (1957–1960), which, as a consequence, also featured a context-free grammar to describe the resulting Algol syntax. This became a standard feature of computer languages, and the notation for grammars used in concrete descriptions of computer languages came to be known as Backus–Naur form, after two members of the Algol language design committee. The "block structure" aspect that context-free grammars capture is so fundamental to grammar that the terms syntax and grammar are often identified with context-free grammar rules, especially in computer science. Formal constraints not captured by the grammar are then considered to be part of the "semantics" of the language.


title: Context-free grammar

text: Context-free grammars are simple enough to allow the construction of efficient parsing algorithms that, for a given string, determine whether and how it can be generated from the grammar. An Earley parser is an example of such an algorithm, while the widely used LR and LL parsers are simpler algorithms that deal only with more restrictive subsets of context-free grammars.


title: Context-free grammar

text: A production rule in is formalized mathematically as a pair formula_11, where formula_12 is a nonterminal and formula_13 is a string of variables and/or terminals; rather than using ordered pair notation, production rules are usually written using an arrow operator with formula_3 as its left hand side and as its right hand side:


title: Context-free grammar

text: It is allowed for to be the empty string, and in this case it is customary to denote it by ε. The form formula_16 is called an -production.


title: Context-free grammar

text: It is common to list all right-hand sides for the same left-hand side on the same line, using | (the vertical bar) to separate them. Rules formula_17 and formula_18 can hence be written as formula_19. In this case, formula_20 and formula_21 are called the first and second alternative, respectively.


title: Context-free grammar

text: For any strings formula_22, we say directly yields , written as formula_23, if formula_24 with formula_12 and formula_26 such that formula_27 and formula_28. Thus, is a result of applying the rule formula_29 to .


title: Context-free grammar

text: For any strings formula_30 we say "yields" or is "derived" from if there is a positive integer and strings formula_31 such that formula_32. This relation is denoted formula_33, or formula_34 in some textbooks. If formula_35, the relation formula_36 holds. In other words, formula_37 and formula_38 are the reflexive transitive closure (allowing a string to yield itself) and the transitive closure (requiring at least one step) of formula_39, respectively.


title: Context-free grammar

text: A language is said to be a context-free language (CFL), if there exists a CFG , such that formula_42.


title: Context-free grammar

text: is context-free. It is not proper since it includes an ε-production. A typical derivation in this grammar is


title: Context-free grammar

text: The canonical example of a context-free grammar is parenthesis matching, which is representative of the general case. There are two terminal symbols "(" and ")" and one nonterminal symbol S. The production rules are


title: Context-free grammar

text: The first rule allows the S symbol to multiply; the second rule allows the S symbol to become enclosed by matching parentheses; and the third rule terminates the recursion.


title: Context-free grammar

text: A second canonical example is two different kinds of matching nested parentheses, described by the productions:


title: Context-free grammar

text: In a context-free grammar, we can pair up characters the way we do with brackets. The simplest example:


title: Context-free grammar

text: This grammar generates the language formula_45, which is not regular (according to the pumping lemma for regular languages).


title: Context-free grammar

text: we obtain a grammar generating the language formula_46 instead. This differs only in that it contains the empty string while the original grammar did not.


title: Context-free grammar

text: A context-free grammar for the language consisting of all strings over {a,b} containing an unequal number of a's and b's:


title: Context-free grammar

text: Here, the nonterminal T can generate all strings with more a's than b's, the nonterminal U generates all strings with more b's than a's and the nonterminal V generates all strings with an equal number of a's and b's. Omitting the third alternative in the rules for T and U doesn't restrict the grammar's language.


title: Context-free grammar

text: Another example of a non-regular language is formula_47. It is context-free as it can be generated by the following context-free grammar:


title: Context-free grammar

text: The formation rules for the terms and formulas of formal logic fit the definition of context-free grammar, except that the set of symbols may be infinite and there may be more than one start symbol.


title: Context-free grammar

text: In contrast to well-formed nested parentheses and square brackets in the previous section, there is no context-free grammar for generating all sequences of two different types of parentheses, each separately balanced "disregarding the other", where the two types need not nest inside one another, for example:


title: Context-free grammar

text: The fact that this language is not context free can be proven using pumping lemma for context-free languages and a proof by contradiction, observing that all words of the form


title: Context-free grammar

text: should belong to the language. This language belongs instead to a more general class and can be described by a conjunctive grammar, which in turn also includes other non-context-free languages, such as the language of all words of the form


title: Context-free grammar

text: Every regular grammar is context-free, but not all context-free grammars are regular. The following context-free grammar, for example, is also regular.


title: Context-free grammar

text: The language described is all nonempty strings of formula_50s and formula_51s that end in formula_50.


title: Context-free grammar

text: This grammar is regular: no rule has more than one nonterminal in its right-hand side, and each of these nonterminals is at the same end of the right-hand side.


title: Context-free grammar

text: Every regular grammar corresponds directly to a nondeterministic finite automaton, so we know that this is a regular language.


title: Context-free grammar

text: A "derivation" of a string for a grammar is a sequence of grammar rule applications that transform the start symbol into the string.


title: Context-free grammar

text: Given such a strategy, a derivation is completely determined by the sequence of rules applied. For instance, one leftmost derivation of the same string is


title: Context-free grammar

text: The distinction between leftmost derivation and rightmost derivation is important because in most parsers the transformation of the input is defined by giving a piece of code for every grammar rule that is executed whenever the rule is applied. Therefore, it is important to know whether the parser determines a leftmost or a rightmost derivation because this determines the order in which the pieces of code will be executed. See for an example LL parsers and LR parsers.


title: Context-free grammar

text: A derivation also imposes in some sense a hierarchical structure on the string that is derived. For example, if the string "1 + 1 + a" is derived according to the leftmost derivation outlined above, the structure of the string would be:


title: Erdős number

text: The Erdős number () describes the "collaborative distance" between mathematician Paul Erdős and another person, as measured by authorship of mathematical papers. The same principle has been applied in other fields where a particular individual has collaborated with a large and broad number of peers.


title: Erdős number

text: Paul Erdős (1913–1996) was an influential Hungarian mathematician who in the latter part of his life spent a great deal of time writing papers with a large number of colleagues, working on solutions to outstanding mathematical problems. He published more papers during his lifetime (at least 1,525) than any other mathematician in history. (Leonhard Euler published more total pages of mathematics but fewer separate papers: about 800.) Erdős spent a large portion of his later life living out of a suitcase, visiting his over 500 collaborators around the world.


title: Erdős number

text: The idea of the Erdős number was originally created by the mathematician's friends as a tribute to his enormous output. Later it gained prominence as a tool to study how mathematicians cooperate to find answers to unsolved problems. Several projects are devoted to studying connectivity among researchers, using the Erdős number as a proxy. For example, Erdős collaboration graphs can tell us how authors cluster, how the number of co-authors per paper evolves over time, or how new theories propagate.


title: Erdős number

text: Several studies have shown that leading mathematicians tend to have particularly low Erdős numbers. The median Erdős number of Fields Medalists is 3. Only 7,097 (about 5% of mathematicians with a collaboration path) have an Erdős number of 2 or lower. As time passes, the lowest Erdős number that can still be achieved will necessarily increase, as mathematicians with low Erdős numbers die and become unavailable for collaboration. Still, historical figures can have low Erdős numbers. For example, renowned Indian mathematician Srinivasa Ramanujan has an Erdős number of only 3 (through G. H. Hardy, Erdős number 2), even though Paul Erdős was only 7 years old when Ramanujan died.


title: Erdős number

text: To be assigned an Erdős number, someone must be a coauthor of a research paper with another person who has a finite Erdős number. Paul Erdős has an Erdős number of zero. Anybody else's Erdős number is where is the lowest Erdős number of any coauthor. The American Mathematical Society provides a free online tool to determine the collaboration distance between two mathematical authors listed in the "Mathematical Reviews" catalogue.


title: Erdős number

text: Erdős wrote around 1,500 mathematical articles in his lifetime, mostly co-written. He had 509 direct collaborators; these are the people with Erdős number 1. The people who have collaborated with them (but not with Erdős himself) have an Erdős number of 2 (12,600 people as of 7 August 2020), those who have collaborated with people who have an Erdős number of 2 (but not with Erdős or anyone with an Erdős number of 1) have an Erdős number of 3, and so forth. A person with no such coauthorship chain connecting to Erdős has an Erdős number of infinity (or an undefined one). Since the death of Paul Erdős, the lowest Erdős number that a new researcher can obtain is 2.


title: Erdős number

text: There is room for ambiguity over what constitutes a link between two authors. The American Mathematical Society collaboration distance calculator uses data from "Mathematical Reviews", which includes most mathematics journals but covers other subjects only in a limited way, and which also includes some non-research publications. The Erdős Number Project web site says: It also says:


title: Erdős number

text: but excludes non-research publications such as elementary textbooks, joint editorships, obituaries, and the like. The "Erdős number of the second kind" restricts assignment of Erdős numbers to papers with only two collaborators.


title: Erdős number

text: The Erdős number was most likely first defined in print by Casper Goffman, an analyst whose own Erdős number is 2. Goffman published his observations about Erdős' prolific collaboration in a 1969 article entitled ""And what is your Erdős number?"" See also some comments in an obituary by Michael Golomb.


title: Erdős number

text: The median Erdős number among Fields medalists is as low as 3. Fields medalists with Erdős number 2 include Atle Selberg, Kunihiko Kodaira, Klaus Roth, Alan Baker, Enrico Bombieri, David Mumford, Charles Fefferman, William Thurston, Shing-Tung Yau, Jean Bourgain, Richard Borcherds, Manjul Bhargava, Jean-Pierre Serre and Terence Tao. There are no Fields medalists with Erdős number 1; however, Endre Szemerédi is an Abel Prize Laureate with Erdős number 1.


title: Erdős number

text: While Erdős collaborated with hundreds of co-authors, there were some individuals with whom he co-authored dozens of papers. This is a list of the ten persons who most frequently co-authored with Erdős and their number of papers co-authored with Erdős (i.e. their number of collaborations).


title: Erdős number

text: , all Fields Medalists have a finite Erdős number, with values that range between 2 and 6, and a median of 3. In contrast, the median Erdős number across all mathematicians (with a finite Erdős number) is 5, with an extreme value of 13. The table below summarizes the Erdős number statistics for Nobel prize laureates in Physics, Chemistry, Medicine and Economics. The first column counts the number of laureates. The second column counts the number of winners with a finite Erdős number. The third column is the percentage of winners with a finite Erdős number. The remaining columns report the minimum, maximum, average and median Erdős numbers among those laureates.


title: Erdős number

text: Among the Nobel Prize laureates in Physics, Albert Einstein and Sheldon Glashow have an Erdős number of 2. Nobel Laureates with an Erdős number of 3 include Enrico Fermi, Otto Stern, Wolfgang Pauli, Max Born, Willis E. Lamb, Eugene Wigner, Richard P. Feynman, Hans A. Bethe, Murray Gell-Mann, Abdus Salam, Steven Weinberg, Norman F. Ramsey, Frank Wilczek, and David Wineland. Fields Medal-winning physicist Ed Witten has an Erdős number of 3.


title: Erdős number

text: Computational biologist Lior Pachter has an Erdős number of 2. Evolutionary biologist Richard Lenski has an Erdős number of 3, having co-authored a publication with Lior Pachter and with mathematician Bernd Sturmfels, each of whom has an Erdős number of 2.


title: Erdős number

text: There are at least two winners of the Nobel Prize in Economics with an Erdős number of 2: Harry M. Markowitz (1990) and Leonid Kantorovich (1975). Other financial mathematicians with Erdős number of 2 include David Donoho, Marc Yor, Henry McKean, Daniel Stroock, and Joseph Keller.


title: Erdős number

text: Nobel Prize laureates in Economics with an Erdős number of 3 include Kenneth J. Arrow (1972), Milton Friedman (1976), Herbert A. Simon (1978), Gerard Debreu (1983), John Forbes Nash, Jr. (1994), James Mirrlees (1996), Daniel McFadden (2000), Daniel Kahneman (2002), Robert J. Aumann (2005), Leonid Hurwicz (2007), Roger Myerson (2007), Alvin E. Roth (2012), and Lloyd S. Shapley (2012) and Jean Tirole (2014).


title: Erdős number

text: Some investment firms have been founded by mathematicians with low Erdős numbers, among them James B. Ax of Axcom Technologies, and James H. Simons of Renaissance Technologies, both with an Erdős number of 3.


title: Erdős number

text: Since the more formal versions of philosophy share reasoning with the basics of mathematics, these fields overlap considerably, and Erdős numbers are available for many philosophers. Philosophers John P. Burgess and Brian Skyrms have an Erdős number of 2. Jon Barwise and Joel David Hamkins, both with Erdős number 2, have also contributed extensively to philosophy, but are primarily described as mathematicians.


title: Erdős number

text: Judge Richard Posner, having coauthored with Alvin E. Roth, has an Erdős number of at most 4. Roberto Mangabeira Unger, a politician, philosopher and legal theorist who teaches at Harvard Law School, has an Erdős number of at most 4, having coauthored with Lee Smolin.


title: Erdős number

text: Some fields of engineering, in particular communication theory and cryptography, make direct use of the discrete mathematics championed by Erdős. It is therefore not surprising that practitioners in these fields have low Erdős numbers. For example, Robert McEliece, a professor of electrical engineering at Caltech, had an Erdős number of 1, having collaborated with Erdős himself. Cryptographers Ron Rivest, Adi Shamir, and Leonard Adleman, inventors of the RSA cryptosystem, all have Erdős number 2.


title: Erdős number

text: The Romanian mathematician and computational linguist Solomon Marcus had an Erdős number of 1 for a paper in "Acta Mathematica Hungarica" that he co-authored with Erdős in 1957.


title: Erdős number

text: Erdős numbers have been a part of the folklore of mathematicians throughout the world for many years. Among all working mathematicians at the turn of the millennium who have a finite Erdős number, the numbers range up to 15, the median is 5, and the mean is 4.65; almost everyone with a finite Erdős number has a number less than 8. Due to the very high frequency of interdisciplinary collaboration in science today, very large numbers of non-mathematicians in many other fields of science also have finite Erdős numbers. For example, political scientist Steven Brams has an Erdős number of 2. In biomedical research, it is common for statisticians to be among the authors of publications, and many statisticians can be linked to Erdős via John Tukey, who has an Erdős number of 2. Similarly, the prominent geneticist Eric Lander and the mathematician Daniel Kleitman have collaborated on papers, and since Kleitman has an Erdős number of 1, a large fraction of the genetics and genomics community can be linked via Lander and his numerous collaborators. Similarly, collaboration with Gustavus Simmons opened the door for


title: Erdős number

text: Erdős numbers within the cryptographic research community, and many linguists have finite Erdős numbers, many due to chains of collaboration with such notable scholars as Noam Chomsky (Erdős number 4), William Labov (3), Mark Liberman (3), Geoffrey Pullum (3), or Ivan Sag (4). There are also connections with arts fields.


title: Erdős number

text: According to Alex Lopez-Ortiz, all the Fields and Nevanlinna prize winners during the three cycles in 1986 to 1994 have Erdős numbers of at most 9.


title: Erdős number

text: Earlier mathematicians published fewer papers than modern ones, and more rarely published jointly written papers. The earliest person known to have a finite Erdős number is either Antoine Lavoisier (born 1743, Erdős number 13), Richard Dedekind (born 1831, Erdős number 7), or Ferdinand Georg Frobenius (born 1849, Erdős number 3), depending on the standard of publication eligibility.


title: Erdős number

text: Martin Tompa proposed a directed graph version of the Erdős number problem, by orienting edges of the collaboration graph from the alphabetically earlier author to the alphabetically later author and defining the "monotone Erdős number" of an author to be the length of a longest path from Erdős to the author in this directed graph. He finds a path of this type of length 12.


title: Erdős number

text: Also, Michael Barr suggests "rational Erdős numbers", generalizing the idea that a person who has written "p" joint papers with Erdős should be assigned Erdős number 1/"p". From the collaboration multigraph of the second kind (although he also has a way to deal with the case of the first kind)—with one edge between two mathematicians for "each" joint paper they have produced—form an electrical network with a one-ohm resistor on each edge. The total resistance between two nodes tells how "close" these two nodes are.


title: Erdős number

text: It has been argued that "for an individual researcher, a measure such as Erdős number captures the structural properties of [the] network whereas the "h"-index captures the citation impact of the publications," and that "One can be easily convinced that ranking in coauthorship networks should take into account both measures to generate a realistic and acceptable ranking."


title: Erdős number

text: In 2004 William Tozier, a mathematician with an Erdős number of 4, auctioned off a co-authorship on eBay, hence providing the buyer with an Erdős number of 5. The winning bid of $1031 was posted by a Spanish mathematician, who however did not intend to pay but just placed the bid to stop what he considered a mockery.


title: Erdős number

text: A number of variations on the concept have been proposed to apply to other fields, notably the Bacon number (as in the game Six Degrees of Kevin Bacon), connecting actors to the actor Kevin Bacon by a chain of joint appearances in films. It was created in 1994, 25 years after Goffman's article on the Erdős number.


title: Erdős number

text: A small number of people are connected to both Erdős and Bacon and thus have an Erdős–Bacon number, which combines the two numbers by taking their sum. One example is the actress-mathematician Danica McKellar, best known for playing Winnie Cooper on the TV series "The Wonder Years".


title: Erdős number

text: Further extension is possible. For example, the "Erdős–Bacon–Sabbath number" is the sum of the Erdős–Bacon number and the collaborative distance to the band Black Sabbath in terms of singing in public. Physicist Stephen Hawking had an Erdős–Bacon–Sabbath number of 8, and actress Natalie Portman has one of 11 (her Erdős number is 5).


title: Erdős number

text: In chess, the Morphy number describes a player's connection to Paul Morphy, widely considered the greatest chess player of his time and an unofficial World Chess Champion.


title: Erdős number

text: In video games, the Ryu number describes a video game character's connection to the Street Fighter character Ryu.


title: Lego Monkie Kid

text: LEGO Monkie Kid () is a LEGO theme inspired by "Monkey King" and "Journey to the West". It is licensed from the LEGO Group. The theme was first introduced in May 2020. The toy line is also accompanied by an animated television series that premiered in China on May 29, 2020, with the special "LEGO Monkie Kid: A Hero Is Born".


title: Lego Monkie Kid

text: "LEGO Monkie Kid" is inspired by "Monkey King" and "Journey to the West", which focuses on Monkie Kid and his friends, battling against a variety of demons who are trying to take over Megapolis.


title: Lego Monkie Kid

text: "LEGO Monkie Kid" is The Lego Group's first product line based on Chinese culture. Although The LEGO Group had previously released LEGO Chinese New Year sets, it was the first time that the company had released an entire product line based on a Chinese theme. Following research in China, The Lego Group discovered that the classic Chinese story of the Monkey King and "Journey to the West" is widely known within Chinese culture. As a result, the story was chosen as the main inspiration for "LEGO Monkie Kid". Simon Lucas, senior creative director commented, "It feels like it was in the DNA of everybody there. So we thought it was a great starting point to tell a new story that's rooted in Chinese culture". The LEGO theme was developed over the course of two years and interpreted the story in a different way to the original. Lucas explained, "The people we spoke to have grown up with these stories, and we wanted to find out what's important to them, and how to interpret that in a new way...So, being 100% accurate to the original was not necessary, really, because we were picking up the key ingredients". The product line does, however, include recognizable characters from "Journey to the West."


title: Lego Monkie Kid

text: The designers behind "LEGO Monkie Kid" had revealed that researching Chinese stories and testing with children were important in the development of the brand new theme. Lego Senior Design Manager Dennis Fong explained, “We felt that we hit something really big when we had this concept of the Monkey King,” and continued, “Seeing all the energy from the kids, the parents, how they could instantly recognize it because we had a lot of key iconic elements in there. And, you know, we didn't need to tell a new story. We had the old story as a foundation for us to build upon."


title: Lego Monkie Kid

text: The initial concept for the theme originated in a rough sketch created by Ned Rogers in December 2021. The sketch depicted several construction sets are transformed into animated vehicles and which parts of the design remain. Featured the concept art are Monkie Kid's Cloud Jet, Pigsy's Food Truck and the Tuk Tuk from Iron Bull Tank. With Lego Monkie Kid theme from The Lego Group was developed as an animated television series, the images showcase how the early set designs were taken and turned into animated models on screens.


title: Lego Monkie Kid

text: The "LEGO Monkie Kid" theme was launched on 16 May 2020. As part of the marketing campaign, The Lego Group released the eight sets inspired by "Monkey King" and "Journey to the West". Each set featured different giant mecha, buildings and vehicles. Minifigures including Monkie Kid, Mei, Monkey King, Mo the cat, Sandy, Mr. Tang and Pigsy were released as well. The sets were designed primarily for children 6+.


title: Lego Monkie Kid

text: In September 2021, Matthew Ashton, The Lego Group's Vice President of Design announced the Monkie Kid alongside City, Friends, Creator, Classic, Technic, Speed Champions, Ninjago, Collectible Minifigures and DOTS themes will continue until at least 2023.


title: Lego Monkie Kid

text: This series also reference other characters from Journey to the West such as Tang Sanzang (唐三藏), Zhu Bajie (豬八戒), Sha Wujing (沙悟淨), the White Dragon Horse (白龍馬), the Buddha (如來佛), Guanyin (觀音), the Jade Emperor (玉皇大帝), the Dragon of the West (西海龍王敖閏), the Rhino King (犀牛王) and the Four Heavenly Kings (四大天王).


title: Lego Monkie Kid

text: According to Bricklink, The Lego Group has released 37 playsets and promotional packs based on the "Lego Monkie Kid" theme.


title: Lego Monkie Kid

text: In 2020, eight sets were released on 16 May 2020 and were based on the TV special titled "A Hero is Born". A total of eight sets including the Monkey King Warrior Mech, Demon Bull King and Monkie Kid's Team Secret HQ were released. Senior Design Director of Lego Simon Lucas discussed about the Demon Bull King set and explained, “The Demon Bull is such an iconic demon and kept coming up in our conversation. So we wanted to include him as the main demon in this season,” and continued, “Then we wanted to reinvent him in a brand new way, because LEGO is the perfect way to do that. So now we heard from the kids, ‘That's definitely the Bull Demon, but I’ve never seen him like that before.” ’ He's now half cyborg and half bull, and that's really cool.” In addition, two promotional polybags namely the Monkie Kid's Delivery Bike and Build Your Own Monkey King were released. On December 31, 2021, A Hero is Born sets got retired in the Lego stores at the end of 2021


title: Lego Monkie Kid

text: In 2020, three sets were released on 1 August 2020 and were based on the first season. A total of three sets including the Monkie Kid's Cloud Roadster were released. On December 31, 2021, the first season sets got retired in the Lego stores at the end of 2021.


title: Lego Monkie Kid

text: In 2021, six sets were released on 1 March 2021 and were based on the second season. A total of six sets including the Monkie Kid's Team Dronecopter and The Legendary Flower Fruit Mountain were released. In addition, Monkie Kid's RC Race and Mini Monkey King Warrior Mech were released as an exclusive set and a promotional polybag respectively. On December 31, 2021, the second season sets got retired in the Lego stores at the end of 2021.


title: Lego Monkie Kid

text: Later, three sets were released on 1 July 2021. A total of three sets including The Bone Demon were released. Senior Creative Director Simon Lucas revealed how the design team took cues from a video game to put together The Bone Demon set and explained, “Lego designer Justin Ramsden and I really tried to make the building journey part of the play,” and continued, “Like a video game, there's a battle at each level, and in the end you face the big boss.” In addition, a two key chains with a key chain attached to the minifigures of Monkie Kid and Red Son. On December 31, 2021, the second season sets got retired in the Lego stores at the end of 2021.


title: Lego Monkie Kid

text: In 2022, seven sets were released on 1 January 2022 and were based on the third season. A total of seven sets including Monkie Kid's Staff Creations, Monkie Kid's Galactic Explorer and The City of Lanterns were released as well. The Lego Group revealed at the China International Import Expo a brand new set titled the "Monkie Kid's Galactic Explorer" where MK and his team have built a rocket to launch into space, but Macaque's shadow clones try to stop them. The Minifigures are Monkie Kid, Mei, Mr. Tang, Sandy (minifig), a Mo space robot, and two of Macaque's shadow clones named Rumble and Savage. In addition, a promotional polybag set namely Monkie Kid's Underwater Journey was released as well. The Lego Group designer Justin Ramsden discussed about The City of Lanterns set and explained, "What's this extra part of track that's included at the back of the Lego model?! If you're lucky enough to get your hands on multiple copies of this set, then with a very small amount of rebuilding, you can actually combine them to make a much larger City!" and explained, "Finally… to some, this may be the luxurious Lotus Hotel however, don't be fooled! This is actually a candle to celebrate my seventh anniversary of working at The Lego Group. Cheers and hope you enjoy the set!"


title: Lego Monkie Kid

text: Later, three sets were released on 1 June 2022. A total of three new sets named the Dragon of the East, Monkie Kid’s Team Van and The Heavenly Realms were released.


title: Lego Monkie Kid

text: In November 2022, The Lego Group revealed at the China International Import Expo a brand new set titled the "Monkey King Ultra Mech" will be released in January 2023. The set consists of 1705 pieces with 6 minifigures. The set included Lego minifigures of Monkey King, Monkie Kid, Mr Tang, Golden-Winged Eagle, Azure Lion and Yellow Tusk Elephant. In addition, five new sets including Monkey King Marketplace, Monkie Kid’s Combi Mech, Mei’s Dragon Jet, Yellow Tusk Elephant and Monkie Kid’s Team Hideout were released as well.


title: Lego Monkie Kid

text: A Monkey King set was released as part of "Lego BrickHeadz" theme on 1 August 2020. The set consists of 175 pieces and a baseplate. The set included a Golden Staff. On December 31, 2021, the set got retired in the Lego stores at the end of 2021.


title: Lego Monkie Kid

text: Lego Monkie Kid is an animated television series series inspired by "Monkey King" and "Journey to the West" and produced by Flying Bark Productions to coincide with the release of the theme's Lego sets. The series premiered on TV3 in Malaysia on 13 September 2020, debuted on Channel 9 in Australia on 13 March 2021 and debuted on CITV in the United Kingdom on 9 May 2022.


title: Lego Monkie Kid

text: "Monkie Kid: A Hero is Born" is a 45-minute television special that premiered on RTM TV2 and TV3 in Malaysia on 13 June 2020, debuted on Mediacorp in Singapore on 27 June 2020, premiered on 9Go! in Australia on 13 March 2021, and premiered internationally on Amazon Kids+ on September 9, 2021. It also debuted on CITV in the United Kingdom on 9 May 2022.


title: Lego Monkie Kid

text: "Revenge of the Spider Queen" is a 43-minute television special that premiered on TV3 in Malaysia on 27 March 2021, premiered on 9Go! in Australia on 24 April 2021, and premiered internationally on Amazon Kids+ on September 30, 2021. It also debuted on CITV in the United Kingdom on 17 May 2022.


title: Lego Monkie Kid

text: "Embrace Your Destiny" is a four-part television special/mini-series that premiered on CITV in the United Kingdom on 1 June 2022.


title: Lego Monkie Kid

text: In November 2021, a Lego Monkie Kid themed land was announced for the upcoming launch of Legoland Shanghai Resort in 2024.


title: Lego Monkie Kid

text: A quarterly Lego Monkie Kid limited edition magazine published by CoroCoro was launched from 2021 to accompany the toy line only available in Japan.


title: Lego Monkie Kid

text: A crossover mobile fighting game named "Lego Brawls" was developed by RED Games. "Lego Brawls" was released exclusively for Apple Arcade on September 19, 2019, for iOS devices, and will be available for PC and Consoles in June 2022. It includes Monkie Kid, Mei, Pigsy, Mr. Tang, Monkey King, Princess Iron Fan, Red Son, a Bull Clone, Gold and Silver Horn Demons, and the Spider Queen as playable characters.


title: Lego Monkie Kid

text: Lego Masters China has started its first season of the regional show, with a trailer showcasing an upcoming episode based on Lego Monkie Kid.


title: Lego Monkie Kid

text: In October 2021, Lego Monkie Kid was nominated for "Animated Series Production of the Year" by the 20th Screen Producers Australia Awards. It was also nominated for the Animation Ages 11–17 category in the 2022 Banff Rockie Awards.


title: Lego Monkie Kid

text: In December 2022, Lego Monkie Kid Director Sarah Harper was awarded for "Best Direction in Animation" by the 2022 Australian Directors’ Guild Awards.


title: Simulated annealing

text: Simulated annealing (SA) is a probabilistic technique for approximating the global optimum of a given function. Specifically, it is a metaheuristic to approximate global optimization in a large search space for an optimization problem. It is often used when the search space is discrete (for example the traveling salesman problem, the boolean satisfiability problem, protein structure prediction, and job-shop scheduling). For problems where finding an approximate global optimum is more important than finding a precise local optimum in a fixed amount of time, simulated annealing may be preferable to exact algorithms such as gradient descent or branch and bound.


title: Simulated annealing

text: The name of the algorithm comes from annealing in metallurgy, a technique involving heating and controlled cooling of a material to alter its physical properties. Both are attributes of the material that depend on their thermodynamic free energy. Heating and cooling the material affects both the temperature and the thermodynamic free energy or Gibbs energy.


title: Simulated annealing

text: Simulated annealing can be used for very hard computational optimization problems where exact algorithms fail; even though it usually achieves an approximate solution to the global minimum, it could be enough for many practical problems.


title: Simulated annealing

text: The problems solved by SA are currently formulated by an objective function of many variables, subject to several constraints. In practice, the constraint can be penalized as part of the objective function.


title: Simulated annealing

text: Similar techniques have been independently introduced on several occasions, including Pincus (1970), Khachaturyan et al (1979, 1981), Kirkpatrick, Gelatt and Vecchi (1983), and Cerny (1985). In 1983, this approach was used by Kirkpatrick, Gelatt Jr., Vecchi, for a solution of the traveling salesman problem. They also proposed its current name, simulated annealing.


title: Simulated annealing

text: This notion of slow cooling implemented in the simulated annealing algorithm is interpreted as a slow decrease in the probability of accepting worse solutions as the solution space is explored. Accepting worse solutions allows for a more extensive search for the global optimal solution. In general, simulated annealing algorithms work as follows. The temperature progressively decreases from an initial positive value to zero. At each time step, the algorithm randomly selects a solution close to the current one, measures its quality, and moves to it according to the temperature-dependent probabilities of selecting better or worse solutions, which during the search respectively remain at 1 (or positive) and decrease toward zero.


title: Simulated annealing

text: The simulation can be performed either by a solution of kinetic equations for density functions or by using the stochastic sampling method. The method is an adaptation of the Metropolis–Hastings algorithm, a Monte Carlo method to generate sample states of a thermodynamic system, published by N. Metropolis et al. in 1953.


title: Simulated annealing

text: The state of some physical systems, and the function "E"("s") to be minimized, is analogous to the internal energy of the system in that state. The goal is to bring the system, from an arbitrary "initial state", to a state with the minimum possible energy.


title: Simulated annealing

text: At each step, the simulated annealing heuristic considers some neighboring state "s*" of the current state "s", and probabilistically decides between moving the system to state "s*" or staying in-state "s". These probabilities ultimately lead the system to move to states of lower energy. Typically this step is repeated until the system reaches a state that is good enough for the application, or until a given computation budget has been exhausted.


title: Simulated annealing

text: Optimization of a solution involves evaluating the neighbours of a state of the problem, which are new states produced through conservatively altering a given state. For example, in the traveling salesman problem each state is typically defined as a permutation of the cities to be visited, and the neighbors of any state are the set of permutations produced by swapping any two of these cities. The well-defined way in which the states are altered to produce neighboring states is called a "move", and different moves give different sets of neighboring states. These moves usually result in minimal alterations of the last state, in an attempt to progressively improve the solution through iteratively improving its parts (such as the city connections in the traveling salesman problem).


title: Simulated annealing

text: Simple heuristics like hill climbing, which move by finding better neighbour after better neighbour and stop when they have reached a solution which has no neighbours that are better solutions, cannot guarantee to lead to any of the existing better solutions their outcome may easily be just a local optimum, while the actual best solution would be a global optimum that could be different. Metaheuristics use the neighbours of a solution as a way to explore the solution space, and although they prefer better neighbours, they also accept worse neighbours in order to avoid getting stuck in local optima; they can find the global optimum if run for a long enough amount of time.


title: Simulated annealing

text: The probability of making the transition from the current state formula_1 to a candidate new state formula_2 is specified by an "acceptance probability function" formula_3, that depends on the energies formula_4 and formula_5 of the two states, and on a global time-varying parameter formula_6 called the "temperature". States with a smaller energy are better than those with a greater energy. The probability function formula_7 must be positive even when formula_8 is greater than formula_9. This feature prevents the method from becoming stuck at a local minimum that is worse than the global one.


title: Simulated annealing

text: When formula_6 tends to zero, the probability formula_3 must tend to zero if formula_12 and to a positive value otherwise. For sufficiently small values of formula_6, the system will then increasingly favor moves that go "downhill" (i.e., to lower energy values), and avoid those that go "uphill." With formula_14 the procedure reduces to the greedy algorithm, which makes only the downhill transitions.


title: Simulated annealing

text: In the original description of simulated annealing, the probability formula_3 was equal to 1 when formula_16—i.e., the procedure always moved downhill when it found a way to do so, irrespective of the temperature. Many descriptions and implementations of simulated annealing still take this condition as part of the method's definition. However, this condition is not essential for the method to work.


title: Simulated annealing

text: The formula_7 function is usually chosen so that the probability of accepting a move decreases when the difference


title: Simulated annealing

text: formula_18 increases—that is, small uphill moves are more likely than large ones. However, this requirement is not strictly necessary, provided that the above requirements are met.


title: Simulated annealing

text: Given these properties, the temperature formula_6 plays a crucial role in controlling the evolution of the state formula_1 of the system with regard to its sensitivity to the variations of system energies. To be precise, for a large formula_6, the evolution of formula_1 is sensitive to coarser energy variations, while it is sensitive to finer energy variations when formula_6 is small.


title: Simulated annealing

text: The name and inspiration of the algorithm demand an interesting feature related to the temperature variation to be embedded in the operational characteristics of the algorithm. This necessitates a gradual reduction of the temperature as the simulation proceeds. The algorithm starts initially with formula_6 set to a high value (or infinity), and then it is decreased at each step following some "annealing schedule"—which may be specified by the user, but must end with formula_14 towards the end of the allotted time budget. In this way, the system is expected to wander initially towards a broad region of the search space containing good solutions, ignoring small features of the energy function; then drift towards low-energy regions that become narrower and narrower, and finally move downhill according to the steepest descent heuristic.


title: Simulated annealing

text: For any given finite problem, the probability that the simulated annealing algorithm terminates with a global optimal solution approaches 1 as the annealing schedule is extended. This theoretical result, however, is not particularly helpful, since the time required to ensure a significant probability of success will usually exceed the time required for a complete search of the solution space.


title: Simulated annealing

text: The following pseudocode presents the simulated annealing heuristic as described above. It starts from a state and continues until a maximum of steps have been taken. In the process, the call should generate a randomly chosen neighbour of a given state ; the call should pick and return a value in the range , uniformly at random. The annealing schedule is defined by the call , which should yield the temperature to use, given the fraction of the time budget that has been expended so far.


title: Simulated annealing

text: In order to apply the simulated annealing method to a specific problem, one must specify the following parameters: the state space, the energy (goal) function , the candidate generator procedure , the acceptance probability function , and the annealing schedule AND initial temperature . These choices can have a significant impact on the method's effectiveness. Unfortunately, there are no choices of these parameters that will be good for all problems, and there is no general way to find the best choices for a given problem. The following sections give some general guidelines.


title: Simulated annealing

text: Simulated annealing may be modeled as a random walk on a search graph, whose vertices are all possible states, and whose edges are the candidate moves. An essential requirement for the function is that it must provide a sufficiently short path on this graph from the initial state to any state which may be the global optimum the diameter of the search graph must be small. In the traveling salesman example above, for instance, the search space for n = 20 cities has n! = 2,432,902,008,176,640,000 (2.4 quintillion) states; yet the number of neighbors of each vertex is formula_26 edges (coming from n choose 2), and the diameter of the graph is formula_27.


title: Simulated annealing

text: To investigate the behavior of simulated annealing on a particular problem, it can be useful to consider the "transition probabilities" that result from the various design choices made in the implementation of the algorithm. For each edge formula_28 of the search graph, the transition probability is defined as the probability that the simulated annealing algorithm will move to state formula_29 when its current state is formula_1. This probability depends on the current temperature as specified by , on the order in which the candidate moves are generated by the function, and on the acceptance probability function . (Note that the transition probability is not simply formula_31, because the candidates are tested serially.)


title: Simulated annealing

text: The specification of , , and is partially redundant. In practice, it's common to use the same acceptance function for many problems, and adjust the other two functions according to the specific problem.


title: Simulated annealing

text: In the formulation of the method by Kirkpatrick et al., the acceptance probability function formula_31 was defined as 1 if formula_33, and formula_34 otherwise. This formula was superficially justified by analogy with the transitions of a physical system; it corresponds to the Metropolis–Hastings algorithm, in the case where T=1 and the proposal distribution of Metropolis–Hastings is symmetric. However, this acceptance probability is often used for simulated annealing even when the function, which is analogous to the proposal distribution in Metropolis–Hastings, is not symmetric, or not probabilistic at all. As a result, the transition probabilities of the simulated annealing algorithm do not correspond to the transitions of the analogous physical system, and the long-term distribution of states at a constant temperature formula_6 need not bear any resemblance to the thermodynamic equilibrium distribution over states of that physical system, at any temperature. Nevertheless, most descriptions of simulated annealing assume the original acceptance function, which is probably hard-coded in many implementations of SA.


title: Simulated annealing

text: In 1990, Moscato and Fontanari, and independently Dueck and Scheuer, proposed that a deterministic update (i.e. one that is not based on the probabilistic acceptance rule) could speed-up the optimization process without impacting on the final quality. Moscato and Fontanari conclude from observing the analogous of the "specific heat" curve of the "threshold updating" annealing originating from their study that "the stochasticity of the Metropolis updating in the simulated annealing algorithm does not play a major role in the search of near-optimal minima". Instead, they proposed that "the smoothening of the cost function landscape at high temperature and the gradual definition of the minima during the cooling process are the fundamental ingredients for the success of simulated annealing." The method subsequently popularized under the denomination of "threshold accepting" due to Dueck and Scheuer's denomination. In 2001, Franz, Hoffmann and Salamon showed that the deterministic update strategy is indeed the optimal one within the large class of algorithms that simulate a random walk on the cost/energy landscape.


title: Simulated annealing

text: When choosing the candidate generator , one must consider that after a few iterations of the simulated annealing algorithm, the current state is expected to have much lower energy than a random state. Therefore, as a general rule, one should skew the generator towards candidate moves where the energy of the destination state formula_29 is likely to be similar to that of the current state. This heuristic (which is the main principle of the Metropolis–Hastings algorithm) tends to exclude "very good" candidate moves as well as "very bad" ones; however, the former are usually much less common than the latter, so the heuristic is generally quite effective.


title: Simulated annealing

text: In the traveling salesman problem above, for example, swapping two "consecutive" cities in a low-energy tour is expected to have a modest effect on its energy (length); whereas swapping two "arbitrary" cities is far more likely to increase its length than to decrease it. Thus, the consecutive-swap neighbour generator is expected to perform better than the arbitrary-swap one, even though the latter could provide a somewhat shorter path to the optimum (with formula_27 swaps, instead of formula_38).


title: Simulated annealing

text: A more precise statement of the heuristic is that one should try first candidate states formula_29 for which formula_40 is large. For the "standard" acceptance function formula_7 above, it means that formula_42 is on the order of formula_6 or less. Thus, in the traveling salesman example above, one could use a function that swaps two random cities, where the probability of choosing a city-pair vanishes as their distance increases beyond formula_6.


title: Simulated annealing

text: When choosing the candidate generator one must also try to reduce the number of "deep" local minima—states (or sets of connected states) that have much lower energy than all its neighbouring states. Such "closed catchment basins" of the energy function may trap the simulated annealing algorithm with high probability (roughly proportional to the number of states in the basin) and for a very long time (roughly exponential on the energy difference between the surrounding states and the bottom of the basin).


title: Simulated annealing

text: As a rule, it is impossible to design a candidate generator that will satisfy this goal and also prioritize candidates with similar energy. On the other hand, one can often vastly improve the efficiency of simulated annealing by relatively simple changes to the generator. In the traveling salesman problem, for instance, it is not hard to exhibit two tours formula_45, formula_46, with nearly equal lengths, such that (1) formula_45 is optimal, (2) every sequence of city-pair swaps that converts formula_45 to formula_46 goes through tours that are much longer than both, and (3) formula_45 can be transformed into formula_46 by flipping (reversing the order of) a set of consecutive cities. In this example, formula_45 and formula_46 lie in different "deep basins" if the generator performs only random pair-swaps; but they will be in the same basin if the generator performs random segment-flips.


title: Simulated annealing

text: The physical analogy that is used to justify simulated annealing assumes that the cooling rate is low enough for the probability distribution of the current state to be near thermodynamic equilibrium at all times. Unfortunately, the "relaxation time"—the time one must wait for the equilibrium to be restored after a change in temperature—strongly depends on the "topography" of the energy function and on the current temperature. In the simulated annealing algorithm, the relaxation time also depends on the candidate generator, in a very complicated way. Note that all these parameters are usually provided as black box functions to the simulated annealing algorithm. Therefore, the ideal cooling rate cannot be determined beforehand, and should be empirically adjusted for each problem. Adaptive simulated annealing algorithms address this problem by connecting the cooling schedule to the search progress. Other adaptive approach as Thermodynamic Simulated Annealing, automatically adjusts the temperature at each step based on the energy difference between the two states, according to the laws of thermodynamics.


title: Simulated annealing

text: Sometimes it is better to move back to a solution that was significantly better rather than always moving from the current state. This process is called "restarting" of simulated annealing. To do this we set codice_1 and codice_2 to codice_3 and codice_4 and perhaps restart the annealing schedule. The decision to restart could be based on several criteria. Notable among these include restarting based on a fixed number of steps, based on whether the current energy is too high compared to the best energy obtained so far, restarting randomly, etc.


title: American Automobile Association

text: American Automobile Association (AAA – commonly pronounced as "Triple A") is a federation of motor clubs throughout North America. AAA is a privately held not-for-profit national member association and service organization with over 60 million members in the United States and Canada. AAA provides services to its members, including roadside assistance and others. Its national headquarters are in Heathrow, Florida.


title: American Automobile Association

text: The American Automobile Association (the "AAA" or "Triple-A") was founded on March 4, 1902, in Chicago, Illinois, in response to a lack of roads and highways suitable for automobiles. At that time, nine motor clubs with a total of 1,500 members banded together to form the AAA. Those individual motor clubs included the Chicago Automobile Club, Automobile Club of America, Automobile Club of New Jersey, and others. The Automobile Club of Buffalo joined in 1903. Winthrop E. Scarritt was its first president. One of the first things the organization advocated for was the building of a cross-country highway.


title: American Automobile Association

text: In 1904, the AAA merged with the very first American automobile organization, the American Motor League, under the direction of the first chairman, Augustus Post.


title: American Automobile Association

text: The first AAA road maps were published in 1905. AAA began printing hotel guides in 1917. The AAA began its School Safety Patrol Program in 1920, the first of the association's driver safety programs, which provided local schools with materials, including badges and ID cards to train and organize students into a patrol force. The AAA Foundation for Traffic Safety, which conducts studies on motorist safety, was established as a separate entity in 1947.


title: American Automobile Association

text: AAA created an organization called the Racing Board, and later known as the Contest Board, in 1902 to officiate the Vanderbilt Cup international automobile race in Long Island, New York. The Racing Board sanctioned the Indianapolis 500 and awarded national racing championships in 1905, 1916, 1920–1941, and 1946–1955. After the 1955 Le Mans disaster, AAA decided that auto racing distracted from its primary goals, and the United States Automobile Club was formed to take over the race sanctioning/officiating. In 2005, AAA re-entered racing as a sponsor of ISC-owned tracks. In 2006, AAA's foray into racing expanded when it made a three-year commitment to sponsor Roush Racing's number 6 car on the NASCAR Nextel Circuit.


title: American Automobile Association

text: In 1935, AAA published Sportsmanlike Driving, the first course outline for high school teachers. In 1936, AAA published the first driver education curriculum for use in high schools (also titled Sportsmanlike Driving, now known as Responsible Driving). AAA has updated its driver training courses throughout the years and many clubs currently offer their own driving schools, or work with other companies to provide AAA's driving curriculum.


title: American Automobile Association

text: Knowing that vehicles pose a hazard to pedestrians, in 1936 AAA began a pedestrian safety program with a grant from the Automotive Safety Foundation. AAA went on to commission and publish (1938) an extensive study of pedestrian safety for the purpose of reducing pedestrian fatalities and injuries. AAA's Pedestrian Protection Program began in 1937 and focuses national attention on pedestrian safety needs by recognizing cities, counties and states that have demonstrated successful pedestrian safety programs.


title: American Automobile Association

text: AAA has also provided services to the U.S. government in times of war. During the 1940s, AAA offered its services to the Advisory Commission of the Council of National Defense in anticipation of becoming involved in World War II. AAA President Thomas P. Henry was appointed consultant in the transportation unit of the Defense Council, and AAA pledged resources, including highway information, to national defense planning efforts as it had during World War I.


title: American Automobile Association

text: Reductions in manufacturing because of the war increased the need for conservation in automobiles and their related products. AAA's efforts at conservation included supporting the manufacture of synthetic rubber in anticipation of a war-related tire/rubber shortage, urging motorists to reduce their driving speed to conserve fuel (1942); and backing a scrap rubber campaign (1942). In 1944, AAA's Keep 'em Rolling campaign sponsored a cross-country tour featuring cars equipped with synthetic tires. The tour demonstrated the reliability of tires made with synthetic rubber. In doing its part to assist in the war effort, AAA placed its mapping facilities at the disposal of the Army department; conducted motor pool driver education (1943); secured an order from the War Production Board that stopped the sale of certain anti-freeze solutions harmful to motors (1943); launched a campaign to alleviate a growing shortage of auto mechanics (1943); monitored tire and gasoline rationing (1943); and established, in cooperation with the Red Cross and military hospitals, a driver training program for veterans with artificial limbs (1944). AAA also assisted in the development of a manual on Uniform Traffic Control Devices and their operation during wartime (1942).


title: American Automobile Association

text: The end of the war brought new needs for motorists and AAA assisted by releasing the film "Traffic Jam Ahead", which outlined a practical program for postwar traffic safety, and publishing Post-war Travel Trends as a public service. In 1946, AAA launched a campaign called "Take It Easy", which was designed to reduce traffic fatalities. Subsequently, fatalities dropped 20 percent below the pre-war figure.


title: American Automobile Association

text: In the 1960s, AAA helped draft the National Traffic and Motor Vehicle Safety Act of 1966, setting safety standards for automobiles, tires, and equipment. AAA also helped draft the Highway Safety Act, specifying standards for motor vehicle inspection and registration, motorcycle safety, driver education, driver licensing, traffic courts, highway design, construction, maintenance, and traffic control devices.


title: American Automobile Association

text: During the oil crisis of the 1970s, the AAA Fuel Gauge Report was created to assist motorists in finding gas stations that had fuel and were open. AAA also began its Gas Watchers program with the endorsement of President Gerald Ford. The Gas Watchers Guide continues to be published to provide simple steps motorists can take to conserve gasoline in their daily driving.


title: American Automobile Association

text: In 1979, President Jimmy Carter appointed AAA President James B. Creal to the National Alcohol Fuels Commission. Creal also chaired a task force on gas rationing and was appointed to President Carter's National Council on Energy Efficiency. AAA representatives serving on President Carter's Alcohol Fuels Commission were requested to sign the Energy Securities Act of 1980. In addition, Creal served on the Industries Advisory Board of Congressional Travel and Tourism Caucus in the early 1980s.


title: American Automobile Association

text: In the 1980s, AAA's mapping services received significant recognition when scenic highways were identified on AAA's sheet maps for the first time. AAA maps were used in the 1984 Louisiana World Exposition where more than 13,000 full-color AAA map images were provided on an optical laser disc for demonstration of an in-car navigation device in the Chrysler Pavilion. And in 1985 the AAA North American Road Atlas was sold at retail for the first time and made the New York Times best-seller paperback list within six weeks. AAA experimented in the 1980s with the On-line Touring Information System (OTIS), which eventually was combined with other automated services under the name AAA Travel Match. The self-service terminal worked like an ATM, with rotating menus and touch-control screens that allowed users to obtain local travel information.


title: American Automobile Association

text: In Congressional hearings held in 1983 on the proposed Motor Vehicle Theft Law Enforcement Act, the Michigan AAA affiliate (then known as Automobile Club of Michigan) presented testimony regarding the rapid growth in average per-vehicle costs of car theft, in support of stamping the vehicle identification number on individual car parts as a deterrent to such theft.


title: American Automobile Association

text: The AAA School Safety Patrol Program and Lifesaving Medal Award won the Presidential Citation Award for Private Sector Initiatives which honors outstanding volunteer projects in 1985. A year later, on February 4, 1986, President Ronald Reagan honored a recipient of AAA's School Safety Patrol Lifesaving Medal in his State of the Union Address.


title: American Automobile Association

text: In 1988, AAA focused its legislative efforts on the Truck & Bus Safety Regulatory Reform Act requiring interstate drivers and equipment to meet federal safety regulations. The act was signed into law in November 1988.


title: American Automobile Association

text: AAA joined government and private-sector companies—the Federal Highway Administration, Avis, General Motors and the Florida Department of Transportation—in 1990 for the Smart Car experiment, also known as the TravTek Project. This test of a computerized in-car navigation and travel information system demonstrated consumer acceptance of telematics technology that would make driving easier and reduce traffic congestion.


title: American Automobile Association

text: A new driver's education program, "Teaching Teens to Drive", was introduced by AAA in 1996 to focus on parent involvement in teen driving education. A year later, in 1997, AAA launched Licensed to Learn, a campaign to increase awareness of the need for graduated driver licensing (GDL) laws in every state. At the outset of the campaign only eight states had enacted GDL laws. Today, all 50 states and the District of Columbia have enacted some form of GDL legislation.


title: American Automobile Association

text: Research in the 1990s led AAA to pursue another issue of importance to US motorists: a transportation crisis resulting from infrastructure that had been under-funded for many years. The Crisis Ahead: America's Aging Highways and Airways research led to AAA helping to shape two pieces of landmark legislation: the Transportation Equity Act for the 21st Century (TEA-21) in 1998 and the Aviation Investment and Reform Act for the 21st Century (AIR-21) in 2000. Both laws embrace the principle that user fees charged to motorists and air travelers should be fully invested in improving and modernizing the nation's surface and air transportation infrastructures.


title: American Automobile Association

text: Because of its work in traffic safety AAA was cited in 1998 as the Clinton Administration's number one traffic safety partner by U.S. Transportation Secretary Rodney Slater. And in 2000, NHTSA presented AAA with a public service award in appreciation of AAA's leadership in the Child Passenger Safety Certification Program, which teaches how to properly install infant/child safety seats, and for its continuing efforts in graduated driver licensing.


title: American Automobile Association

text: Skyrocketing gas prices led AAA to testify before three Congressional committees regarding increased gasoline prices in 2000, and to lobby to prevent Congress from repealing parts of the federal gasoline tax, which would have reduced Highway Trust Fund revenue without guaranteeing consumers any relief from high gas prices. Participating in the U.S. Department of Transportation secretary's Aviation Summit, AAA President and CEO Robert L. Darbelnet communicated AAA's stand on the aviation crisis saying that consistent underfunding of the nation's air transportation infrastructure had led to the crisis and offering a four-point plan to help turn it around. Also that year, AAA testified before Congress and the Federal Motor Carrier Safety Administration, on proposed hours-of-service regulations for commercial truck drivers and launched Share With Care, a public education campaign on safely sharing the road with trucks.


title: American Automobile Association

text: In the early 2000s (decade), AAA's focus on helping seniors stay mobile longer and more safely led to an appointment to the White House Conference on Aging. AAA promoted solutions such as senior-friendly road design, screening tools, education for seniors and their families, and supplemental transportation. Reader's Digest highlighted AAA's transportation safety agenda by focusing on the importance of road safety improvements, particularly for seniors. To help seniors become safer drivers or to recognize signs that it's time to stop driving, AAA developed Roadwise Review, a computer-based screening tool enabling older drivers to identify and address physiological changes that could affect driving.


title: American Automobile Association

text: During the Jim Crow era, AAA actively discriminated against African Americans, who could not join the association. Alternatives to AAA guides, such as "The Negro Motorist Green Book", were written.


title: American Automobile Association

text: Members belong to one of 42 individual clubs (see List of AAA regional clubs), and the clubs in turn own AAA. The number of local clubs has decreased over time through consolidation; as late as the 1970s the membership roster included dozens of clubs that each served a single county, particularly in New York, Ohio and Pennsylvania. The member clubs have arranged a reciprocal service system so that members of any participating club are able to receive member services from any other affiliate club. Member dues finance all club services as well as the operations of the national organization.


title: American Automobile Association

text: The vast majority of AAA clubs have "AAA" as part of their name, although the two largest AAA clubs by membership do not: the Automobile Club of Southern California and Auto Club Group.


title: American Automobile Association

text: AAA clubs primarily provide emergency road services to its members. These services, which include towing, lockouts, winching, tire changes, automotive first aid, battery replacement, and others, are handled by private local towing companies contracted by a state AAA club. AAA sells roadside assistance for a variety of motor vehicles, including motorcycles. In some areas, AAA also offers bicycle roadside assistance. Many AAA clubs have an automotive fleet division serving large metro areas, while private towing companies cover the surplus call volume by area. Certain clubs have implemented an "on the go" diagnostic/installation automotive battery program.


title: American Automobile Association

text: Clubs also distribute road maps (including customized map guides for specific journeys) and travel publications (TourBook guides), and rate restaurants and hotels according to a "diamond" scale (one to five). The AAA Diamond Program includes over 60,000 properties in the United States, Canada, Mexico and the Caribbean, it is composed of nearly 27,000 hotels and more than 30,000 restaurants. The best hotels and restaurants according to AAA's criteria receive the Five Diamond Award. Many offices sell automobile liability insurance, provide travel agency, auto-registration and notary services. Maps, TourBook guides, and travel agent services are generally free to members. AAA also offers member discounts through its "AAA Discounts & Rewards" program. TripTik is AAA's travel planning guide and online travel planner. The print version includes road maps and other travel information, such as gas prices.


title: American Automobile Association

text: AAA is authorized by the U.S. Department of State to issue International Driving Permits in the United States, along with the National Automobile Club.


title: American Automobile Association

text: The AAA has reciprocal arrangements with a range of international affiliates. In general, members of affiliates are offered the same benefits as members of the AAA while traveling in the United States, while AAA members are offered equivalent benefits while traveling in the territory of the affiliate.


title: American Automobile Association

text: The AAA is known for occasional high-profile motorist advisories of traffic enforcement, such as when it rented a billboard to warn motorists of the speed trap town of Lawtey, Florida. It also is a supporter of the Motor Vehicle Owners' Right to Repair Act, first introduced in 2001 but which has not become law.


title: American Automobile Association

text: Additionally, the AAA supported measures that tax motorists—with the goal of strengthening infrastructure and highway maintenance—as well as supported measures that curtail motorists' legal rights:


title: American Automobile Association

text: In 2001, AAA launched its Great Battery Roundup to encourage motorists to recycle old automobile batteries, tires and various types of automotive fluids. Since then more than 4 million batteries have been recycled through that program and the mobile battery service. Typically holding events around Earth Day, AAA clubs often team up with other environmental organization such as the EPA and the Nature Conservancy to expand these recycling efforts.


title: American Automobile Association

text: In 2006, AAA worked with the EPA to improve the fuel economy information provided to new car buyers by vehicle manufacturers. Using several different types of tests, AAA recreated real-world driving conditions to illustrate the difference in fuel economy, and the EPA incorporated AAA's testing into their new procedures. The more accurate testing resulted in a reduction of miles per gallon claims between 5 and 25 percent, beginning with 2008 model year vehicles.