This problem is also known as "Boolean or propositional satisfiability". Computer scientists usually call it SAT. Complexity theory believes that the formula should be in a special form, known as conjunctive normal form. A formula that is in this form has clauses. Clauses are joined by a "logical and". Each clause has several literals. They are joined by a "logical or". A literal and its complement cannot appear in the same clause. The problem may also have other names. The names depend on what the logical formula looks like. The names also depend on how many variables are used per clause.
A formula that satisfies 3SAT looks like the following:
In this case "("A" OR "B" OR "C")" is an example for a clause, and "B" is one of the literals of this clause.
At the beginning of the 1970s, Stephen Cook and Leonid Levin showed that the problem is NP-complete. This is known as the Cook–Levin theorem.
The problem 3SAT uses three variables per clause. It is one of the 21 NP-complete problems. They were defined by Richard Karp in 1972.
Denny Lemaster
Denver Clayton Lemaster (born February 25, 1939 in Corona, California) was a Major League Baseball pitcher. He began his career when he was signed by the Milwaukee Braves. He spent 1958-early 1962 in the minors. He joined the Braves in 1962, and pitched his first game on June 15th. He played with the Braves until 1967. They had moved to Atlanta by that time. After the 1967 season he was traded to the Astros with Denis Menke. The Braves were given Sonny Jackson and Chuck Harrison. Lemaster played with the Astros for four years. He was then sold to the Montreal Expos, but was released halfway through the season.
NP-complete
An NP problem is an algorithmic problem such that if you have a case of the problem of size formula_1, the number of steps needed to check the answer is smaller than the value of some polynomial in formula_1. It doesn't mean one can find an answer in the polynomial number of steps, only check it.
An NP-complete problem is an NP problem such that if one could find answers to that problem in polynomial number of steps, one could also find answers to all NP problems in polynomial number of steps. This makes NP-complete decision problems the hardest problems in NP (they are NP-hard). People spent lots of time looking for algorithms that finds answers to some NP-complete problem in polynomial number of steps, but have not found any. Because of this, if someone shows a problem to be NP-complete, it is not likely that there is an algorithm solving it in polynomial number of steps.
The unsolved problem P = NP asks whether polynomial time algorithms actually exist for NP-complete, and by corollary, all NP problems. It is widely believed that this is not the case.
The Travelling salesman problem is an NP-Complete problem.
Cook–Levin theorem
The Cook–Levin theorem is a theorem from theoretical computer science, which says that the Boolean satisfiability problem is NP-complete. A deterministic Turing machine can change a problem in NP in polynomial time to the problem of determining whether a Boolean formula is satisfiable. An important consequence of the theorem is that if there exists a deterministic polynomial time algorithm for solving Boolean satisfiability, then there exists a deterministic polynomial time algorithm for solving "all" problems in NP. The same follows for any NP-complete problem.
The question of whether such an algorithm exists is called the P versus NP problem and it is widely considered the most important unsolved problem in theoretical computer science. The theorem is named after Stephen Cook and Leonid Levin, who first described it in the 1970s.
Bill France, Sr.
William Henry Getty France Sr. (September 26, 1909 – June 7, 1992) was an American racecar driver, best known for being the co-founder of NASCAR. France was born in Washington, D.C.. He is also known as the creator of the Daytona International Speedway and the Talladega Superspeedway. France was put into the NASCAR Hall of Fame on May 23 2010.
France was the father of Bill France, Jr. (1933-2007) and grandfather of Brian France.
Denis Menke
Denis John Menke (July 21, 1940 – December 1, 2020) was a professional baseball infielder.
He was born on July 23, 1940, in Bancroft, Iowa. He was signed by the Milwaukee Braves in 1958. He came to the major leagues in 1962.
He became a regular player in 1963. He was traded with Denny Lemaster to the Astros in 1967. He played for Houston for four years, and was elected to the All-Star team as a backup player twice. He was then part of an eight-player trade the Astros made with the Reds. The trade was Menke, Ed Armbrister, Jack Billingham, Cesar Geronimo, and future Hall-of-Famer Joe Morgan for All-star Lee May, All-star Tommy Helms, and Jimmy Stewart.
He played in the 1972 World Series. He batted .083 in 24 at-bats.
Menke died at his home in Tarpon Springs, Florida on December 1, 2020 at the age of 80.
Huaso
A huaso (feminine huasa, but most commonly china) is a Chilean countryman and skilled horseman, very similar to the gauchos, cowboys, vaqueros and charros. Huasos are found in central and southern Chile.
Huasos are an important part of the culture of Chile, and are a vital part of parades, parties, and holidays. The Region of O'Higgins is the place where are found the most of the Chilean huasos.
Purchase
Purchasing is the buying of goods or services. An item that has been bought is called a purchase. The opposite of a purchase is a sale. In common usage, the shorter word "buy" is typically used when shopping, rather than the word "purchase".
However, the word has been used in many major historical terms, including:
The word "purchase" is often used in contracts with "acquisition", as in the term "Acquisitions and Mergers" (A&M) in legal agreements made between large companies. Those contracts typically state than a company was "purchased" by another company.
Stargate (movie)
Stargate is a 1994 science fiction movie.
In a dig at Giza in 1928, scientists find a big metalic ring inscribed with hieroglyphics. Archeologist Doctor Daniel Jackson is called by the US Air Force to translate hieroglyphics on the ring. They find out that the ring is actually a piece of alien technology that creates wormholes to transport people across the universe. A military team goes through the stargate with Jackson, and after the journey find out that they cannot get back to earth. They find a city of ancient Egyptian-like people under the rule of Ra, who is an alien posing as their god. They eventually kill Ra with a nuclear blast and figure out how to get back to earth, but Jackson gets married and stays on the planet.
Super Junior
Super Junior (Korean: 슈퍼주니어), also known as SJ or SuJu is a South Korean boy band, under S.M. Entertainment. It consists of thirteen members, consisting of leader Leeteuk, Heechul, Hankyung, Yesung, Shindong, Sungmin, Eunhyuk, Donghae, Siwon, Ryeowook and Kibum. Kyuhyun joined the group in 2006. Han Geng and Kibum had left SM Entertainment and Super Junior in 2009 and 2015. Kangin left Super Junior voluntarily in 2019 but his exclusive contract with label SJ still remains.
They have released nine albums: Super Junior 05 (TWINS) with only twelve members. Kyuhyun joined later during the release of the song "U". They then released with the full set of thirteen members: Don't Don in 2007; Sorry, Sorry in 2009. Sorry, Sorry excludes Kangin due to suspension. In 2010, they released Bonamana which excludes Kangin, Han Geng, and Kibum. Super Junior then released Mr. Simple in 2011; Sexy, Free & Single in 2012; Hero in 2013; Mamacita in 2014 and Devil in 2015.