paragraph_text: Decision problems are one of the central objects of study in computational complexity theory. A decision problem is a special type of computational problem whose answer is either yes or no, or alternately either 1 or 0. A decision problem can be viewed as a formal language, where the members of the language are instances whose output is yes, and the non-members are those instances whose output is no. The objective is to decide, with the aid of an algorithm, whether a given input string is a member of the formal language under consideration. If the algorithm deciding this problem returns the answer yes, the algorithm is said to accept the input string, otherwise it is said to reject the input.

paragraph_text: The status of "language" is not solely determined by linguistic criteria, but it is also the result of a historical and political development. Romansh came to be a written language, and therefore it is recognized as a language, even though it is very close to the Lombardic alpine dialects. An opposite example is the case of Chinese, whose variations such as Mandarin and Cantonese are often called dialects and not languages, despite their mutual unintelligibility.

paragraph_text: In mathematics, the Pompeiu problem is a conjecture in integral geometry, named for Dimitrie Pompeiu, who posed the problem in 1929,

paragraph_text: Just as the navigational approach would require programs to loop in order to collect records, the relational approach would require loops to collect information about any one record. Codd's solution to the necessary looping was a set-oriented language, a suggestion that would later spawn the ubiquitous SQL. Using a branch of mathematics known as tuple calculus, he demonstrated that such a system could support all the operations of normal databases (inserting, updating etc.) as well as providing a simple system for finding and returning sets of data in a single operation.

paragraph_text: The Analytical Engine was a proposed mechanical general - purpose computer designed by English mathematician and computer pioneer Charles Babbage. It was first described in 1837 as the successor to Babbage's difference engine, a design for a mechanical computer. The Analytical Engine incorporated an arithmetic logic unit, control flow in the form of conditional branching and loops, and integrated memory, making it the first design for a general - purpose computer that could be described in modern terms as Turing - complete. In other words, the logical structure of the Analytical Engine was essentially the same as that which has dominated computer design in the electronic era.

paragraph_text: Damage to a German steel facility occurred during a DST transition in 1993, when a computer timing system linked to a radio time synchronization signal allowed molten steel to cool for one hour less than the required duration, resulting in spattering of molten steel when it was poured. Medical devices may generate adverse events that could harm patients, without being obvious to clinicians responsible for care. These problems are compounded when the DST rules themselves change; software developers must test and perhaps modify many programs, and users must install updates and restart applications. Consumers must update devices such as programmable thermostats with the correct DST rules, or manually adjust the devices' clocks. A common strategy to resolve these problems in computer systems is to express time using the Coordinated Universal Time (UTC) rather than the local time zone. For example, Unix-based computer systems use the UTC-based Unix time internally.

paragraph_text: Grace Murray Hopper Park is a small memorial park in Arlington, Virginia. The park is named in honor of Grace Hopper, a computer scientist and naval officer. A pioneer in the field, she was the first programmer of the Mark I Calculator and developed the first compiler for a computer programming language.

paragraph_text: MySQL ( "My S-Q-L") is an open-source relational database management system (RDBMS).  Its name is a combination of "My", the name of co-founder Michael Widenius's daughter, and "SQL", the abbreviation for Structured Query Language.

paragraph_text: A problem is regarded as inherently difficult if its solution requires significant resources, whatever the algorithm used. The theory formalizes this intuition, by introducing mathematical models of computation to study these problems and quantifying the amount of resources needed to solve them, such as time and storage. Other complexity measures are also used, such as the amount of communication (used in communication complexity), the number of gates in a circuit (used in circuit complexity) and the number of processors (used in parallel computing). One of the roles of computational complexity theory is to determine the practical limits on what computers can and cannot do.

paragraph_text: But bounding the computation time above by some concrete function f(n) often yields complexity classes that depend on the chosen machine model. For instance, the language {xx | x is any binary string} can be solved in linear time on a multi-tape Turing machine, but necessarily requires quadratic time in the model of single-tape Turing machines. If we allow polynomial variations in running time, Cobham-Edmonds thesis states that "the time complexities in any two reasonable and general models of computation are polynomially related" (Goldreich 2008, Chapter 1.2). This forms the basis for the complexity class P, which is the set of decision problems solvable by a deterministic Turing machine within polynomial time. The corresponding set of function problems is FP.

paragraph_text: Problems that can be solved in theory (e.g., given large but finite time), but which in practice take too long for their solutions to be useful, are known as intractable problems. In complexity theory, problems that lack polynomial-time solutions are considered to be intractable for more than the smallest inputs. In fact, the Cobham–Edmonds thesis states that only those problems that can be solved in polynomial time can be feasibly computed on some computational device. Problems that are known to be intractable in this sense include those that are EXPTIME-hard. If NP is not the same as P, then the NP-complete problems are also intractable in this sense. To see why exponential-time algorithms might be unusable in practice, consider a program that makes 2n operations before halting. For small n, say 100, and assuming for the sake of example that the computer does 1012 operations each second, the program would run for about 4 × 1010 years, which is the same order of magnitude as the age of the universe. Even with a much faster computer, the program would only be useful for very small instances and in that sense the intractability of a problem is somewhat independent of technological progress. Nevertheless, a polynomial time algorithm is not always practical. If its running time is, say, n15, it is unreasonable to consider it efficient and it is still useless except on small instances.

paragraph_text: In complexity theory, computational problems that are co-NP-complete are those that are the hardest problems in co-NP, in the sense that any problem in co-NP can be reformulated as a special case of any co-NP-complete problem with only polynomial overhead. If P is different from co-NP, then all of the co-NP-complete problems are not solvable in polynomial time. If there exists a way to solve a co-NP-complete problem quickly, then that algorithm can be used to solve all co-NP problems quickly.

paragraph_text: In control theory and stability theory, the Nyquist stability criterion or Strecker–Nyquist stability criterion, independently discovered by the German electrical engineer at Siemens in 1930 and the Swedish-American electrical engineer Harry Nyquist at Bell Telephone Laboratories in 1932, is a graphical technique for determining the stability of a dynamical system. Because it only looks at the Nyquist plot of the open loop systems, it can be applied without explicitly computing the poles and zeros of either the closed-loop or open-loop system (although the number of each type of right-half-plane singularities must be known). As a result, it can be applied to systems defined by non-rational functions, such as systems with delays. In contrast to Bode plots, it can handle transfer functions with right half-plane singularities. In addition, there is a natural generalization to more complex systems with multiple inputs and multiple outputs, such as control systems for airplanes.

paragraph_text: By 1988, industry observers stated that the NES's popularity had grown so quickly that the market for Nintendo cartridges was larger than that for all home computer software. Compute! reported in 1989 that Nintendo had sold seven million NES systems in 1988, almost as many as the number of Commodore 64s sold in its first five years. "Computer game makers [are] scared stiff", the magazine said, stating that Nintendo's popularity caused most competitors to have poor sales during the previous Christmas and resulted in serious financial problems for some.

paragraph_text: A Turing machine is a mathematical model of a general computing machine. It is a theoretical device that manipulates symbols contained on a strip of tape. Turing machines are not intended as a practical computing technology, but rather as a thought experiment representing a computing machine—anything from an advanced supercomputer to a mathematician with a pencil and paper. It is believed that if a problem can be solved by an algorithm, there exists a Turing machine that solves the problem. Indeed, this is the statement of the Church–Turing thesis. Furthermore, it is known that everything that can be computed on other models of computation known to us today, such as a RAM machine, Conway's Game of Life, cellular automata or any programming language can be computed on a Turing machine. Since Turing machines are easy to analyze mathematically, and are believed to be as powerful as any other model of computation, the Turing machine is the most commonly used model in complexity theory.

paragraph_text: Feynman had a great deal of success teaching Carl, using, for example, discussions about ants and Martians as a device for gaining perspective on problems and issues. He was surprised to learn that the same teaching devices were not useful with Michelle. Mathematics was a common interest for father and son; they both entered the computer field as consultants and were involved in advancing a new method of using multiple computers to solve complex problems—later known as parallel computing. The Jet Propulsion Laboratory retained Feynman as a computational consultant during critical missions. One co-worker characterized Feynman as akin to Don Quixote at his desk, rather than at a computer workstation, ready to do battle with the windmills.

paragraph_text: Gerald Jay Sussman (born February 8, 1947) is the Panasonic Professor of Electrical Engineering at the Massachusetts Institute of Technology (MIT). He received his S.B. and Ph.D. degrees in mathematics from MIT in 1968 and 1973 respectively. He has been involved in artificial intelligence research at MIT since 1964. His research has centered on understanding the problem-solving strategies used by scientists and engineers, with the goals of automating parts of the process and formalizing it to provide more effective methods of science and engineering education. Sussman has also worked in computer languages, in computer architecture and in VLSI design.

paragraph_text: The principle of the modern computer was first described by mathematician and pioneering computer scientist Alan Turing, who set out the idea in his seminal 1936 paper, On Computable Numbers. Turing reformulated Kurt Gödel's 1931 results on the limits of proof and computation, replacing Gödel's universal arithmetic-based formal language with the formal and simple hypothetical devices that became known as Turing machines. He proved that some such machine would be capable of performing any conceivable mathematical computation if it were representable as an algorithm. He went on to prove that there was no solution to the Entscheidungsproblem by first showing that the halting problem for Turing machines is undecidable: in general, it is not possible to decide algorithmically whether a given Turing machine will ever halt.

paragraph_text: The central oscillator generates a self-sustaining rhythm and is driven by two interacting feedback loops that are active at different times of day. The morning loop consists of CCA1 (Circadian and Clock-Associated 1) and LHY (Late Elongated Hypocotyl), which encode closely related MYB transcription factors that regulate circadian rhythms in Arabidopsis, as well as PRR 7 and 9 (Pseudo-Response Regulators.) The evening loop consists of GI (Gigantea) and ELF4, both involved in regulation of flowering time genes. When CCA1 and LHY are overexpressed (under constant light or dark conditions), plants become arrhythmic, and mRNA signals reduce, contributing to a negative feedback loop. Gene expression of CCA1 and LHY oscillates and peaks in the early morning, whereas TOC1 gene expression oscillates and peaks in the early evening. While it was previously hypothesised that these three genes model a negative feedback loop in which over-expressed CCA1 and LHY repress TOC1 and over-expressed TOC1 is a positive regulator of CCA1 and LHY, it was shown in 2012 by Andrew Millar and others that TOC1 in fact serves as a repressor not only of CCA1, LHY, and PRR7 and 9 in the morning loop but also of GI and ELF4 in the evening loop. This finding and further computational modeling of TOC1 gene functions and interactions suggest a reframing of the plant circadian clock as a triple negative-component repressilator model rather than the positive/negative-element feedback loop characterizing the clock in mammals.

paragraph_text: To further highlight the difference between a problem and an instance, consider the following instance of the decision version of the traveling salesman problem: Is there a route of at most 2000 kilometres passing through all of Germany's 15 largest cities? The quantitative answer to this particular problem instance is of little use for solving other instances of the problem, such as asking for a round trip through all sites in Milan whose total length is at most 10 km. For this reason, complexity theory addresses computational problems and not particular problem instances.

Question: The computer language that came about as a result of the looping problem, is partially named after whom?
Answer: Michael Widenius's daughter