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Stephen C. Kleene
Stephen Cole Kleene ( ; January 5, 1909 – January 25, 1994) was an American mathematician. One of the students of Alonzo Church, Kleene, along with Rózsa Péter, Alan Turing, Emil Post, and others, is best known as a founder of the branch of mathematical logic known as recursion theory, which subsequently helped to provide the foundations of theoretical computer science. Kleene's work grounds the study of computable functions. A number of mathematical concepts are named after him: Kleene hierarchy, Kleene algebra, the Kleene star (Kleene closure), Kleene's recursion theorem and the Kleene fixed-point theorem. He also invented regular expressions in 1951 to describe artificial neural network, McCulloch-Pitts neural networks, and made significant contributions to the foundations of mathematical intuitionism. Biography Kleene was awarded a bachelor's degree from Amherst College in 1930. He was awarded a Ph.D. in mathematics from Princeton University in 1934, where his thesis, ent ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Hartford, Connecticut
Hartford is the capital city of the U.S. state of Connecticut. It was the seat of Hartford County until Connecticut disbanded county government in 1960. It is the core city in the Greater Hartford metropolitan area. Census estimates since the 2010 United States census have indicated that Hartford is the fourth-largest city in Connecticut with a 2020 population of 121,054, behind the coastal cities of Bridgeport, New Haven, and Stamford. Hartford was founded in 1635 and is among the oldest cities in the United States. It is home to the country's oldest public art museum (Wadsworth Atheneum), the oldest publicly funded park (Bushnell Park), the oldest continuously published newspaper (the ''Hartford Courant''), and the second-oldest secondary school (Hartford Public High School). It is also home to the Mark Twain House, where the author wrote his most famous works and raised his family, among other historically significant sites. Mark Twain wrote in 1868, "Of all the beautifu ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Kleene's Algorithm
In theoretical computer science, in particular in formal language theory, Kleene's algorithm transforms a given nondeterministic finite automaton (NFA) into a regular expression. Together with other conversion algorithms, it establishes the equivalence of several description formats for regular languages. Alternative presentations of the same method include the "elimination method" attributed to Brzozowski and McCluskey, the algorithm of McNaughton and Yamada, and the use of Arden's lemma. Algorithm description According to Gross and Yellen (2004), Here: sect.2.1, remark R13 on p.65 the algorithm can be traced back to Kleene (1956). A presentation of the algorithm in the case of deterministic finite automata (DFAs) is given in Hopcroft and Ullman (1979). The presentation of the algorithm for NFAs below follows Gross and Yellen (2004). Given a nondeterministic finite automaton ''M'' = (''Q'', Σ, δ, ''q''0, ''F''), with ''Q'' = its set of states, the algorithm computes :the se ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Theoretical Computer Science
Theoretical computer science (TCS) is a subset of general computer science and mathematics that focuses on mathematical aspects of computer science such as the theory of computation, lambda calculus, and type theory. It is difficult to circumscribe the theoretical areas precisely. The Association for Computing Machinery, ACM's ACM SIGACT, Special Interest Group on Algorithms and Computation Theory (SIGACT) provides the following description: History While logical inference and mathematical proof had existed previously, in 1931 Kurt Gödel proved with his incompleteness theorem that there are fundamental limitations on what statements could be proved or disproved. Information theory was added to the field with a 1948 mathematical theory of communication by Claude Shannon. In the same decade, Donald Hebb introduced a mathematical model of Hebbian learning, learning in the brain. With mounting biological data supporting this hypothesis with some modification, the fields of n ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion Theory
Computability theory, also known as recursion theory, is a branch of mathematical logic, computer science, and the theory of computation that originated in the 1930s with the study of computable functions and Turing degrees. The field has since expanded to include the study of generalized computability and definability. In these areas, computability theory overlaps with proof theory and effective descriptive set theory. Basic questions addressed by computability theory include: * What does it mean for a function on the natural numbers to be computable? * How can noncomputable functions be classified into a hierarchy based on their level of noncomputability? Although there is considerable overlap in terms of knowledge and methods, mathematical computability theorists study the theory of relative computability, reducibility notions, and degree structures; those in the computer science field focus on the theory of subrecursive hierarchies, formal methods, and formal languages. I ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematical Logic
Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of formal systems of logic such as their expressive or deductive power. However, it can also include uses of logic to characterize correct mathematical reasoning or to establish foundations of mathematics. Since its inception, mathematical logic has both contributed to and been motivated by the study of foundations of mathematics. This study began in the late 19th century with the development of axiomatic frameworks for geometry, arithmetic, and Mathematical analysis, analysis. In the early 20th century it was shaped by David Hilbert's Hilbert's program, program to prove the consistency of foundational theories. Results of Kurt Gödel, Gerhard Gentzen, and others provided partial resolution to the program, and clarified the issues involved in pr ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Emil Post
Emil Leon Post (; February 11, 1897 – April 21, 1954) was an American mathematician and logician. He is best known for his work in the field that eventually became known as computability theory. Life Post was born in Augustów, Suwałki Governorate, Congress Poland, Russian Empire (now Poland) into a Polish-Jewish family that immigrated to New York City in May 1904. His parents were Arnold and Pearl Post. Post had been interested in astronomy, but at the age of twelve lost his left arm in a car accident. This loss was a significant obstacle to being a professional astronomer, leading to his decision to pursue mathematics rather than astronomy. Post attended the Townsend Harris High School and continued on to graduate from City College of New York in 1917 with a B.S. in Mathematics. After completing his Ph.D. in mathematics in 1920 at Columbia University, supervised by Cassius Jackson Keyser, he did a post-doctorate at Princeton University in the 1920–1921 academic year. Pos ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Alan Turing
Alan Mathison Turing (; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher, and theoretical biologist. Turing was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation with the Turing machine, which can be considered a model of a general-purpose computer. He is widely considered to be the father of theoretical computer science and artificial intelligence. Born in Maida Vale, London, Turing was raised in southern England. He graduated at King's College, Cambridge, with a degree in mathematics. Whilst he was a fellow at Cambridge, he published a proof demonstrating that some purely mathematical yes–no questions can never be answered by computation and defined a Turing machine, and went on to prove that the halting problem for Turing machines is undecidable. In 1938, he obtained his PhD from the Department of Mathemati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Rózsa Péter
Rózsa Péter, born Rózsa Politzer, (17 February 1905 – 16 February 1977) was a Hungarian mathematician and logician. She is best known as the "founding mother of recursion theory". Early life and education Péter was born in Budapest, Hungary, as Rózsa Politzer (Hungarian: Politzer Rózsa). She attended Pázmány Péter University (now Eötvös Loránd University), originally studying chemistry but later switching to mathematics. She attended lectures by Lipót Fejér and József Kürschák. While at university, she met László Kalmár; they would collaborate in future years and Kalmár encouraged her to pursue her love of mathematics. After graduating in 1927, Péter could not find a permanent teaching position although she had passed her exams to qualify as a mathematics teacher. Due to the effects of the Great Depression, many university graduates could not find work and Péter began private tutoring. At this time, she also began her graduate studies. Professional ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Mathematician
A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History One of the earliest known mathematicians were Thales of Miletus (c. 624–c.546 BC); he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed. He is credited with the first use of deductive reasoning applied to geometry, by deriving four corollaries to Thales' Theorem. The number of known mathematicians grew when Pythagoras of Samos (c. 582–c. 507 BC) established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was "All is number". It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins. The first woman mathematician recorded by history was Hypati ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
National Medal Of Science
The National Medal of Science is an honor bestowed by the President of the United States to individuals in science and engineering who have made important contributions to the advancement of knowledge in the fields of behavioral and social sciences, biology, chemistry, engineering, mathematics and physics. The twelve member presidential Committee on the National Medal of Science is responsible for selecting award recipients and is administered by the National Science Foundation (NSF). History The National Medal of Science was established on August 25, 1959, by an act of the Congress of the United States under . The medal was originally to honor scientists in the fields of the "physical, biological, mathematical, or engineering sciences". The Committee on the National Medal of Science was established on August 23, 1961, by executive order 10961 of President John F. Kennedy. On January 7, 1979, the American Association for the Advancement of Science (AAAS) passed a resolution propo ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Leroy P
Leroy or Le Roy may refer to: People * Leroy (name), a given name and surname * Leroy (musician), American musician * Leroy (sailor), French sailor Places United States * Leroy, Alabama * Le Roy, Illinois * Le Roy, Iowa * Le Roy, Kansas * Le Roy, Michigan * Le Roy, Minnesota * Le Roy (town), New York ** Le Roy (village), New York * Leroy, Indiana * Leroy, Texas * LeRoy, Wisconsin, a town * LeRoy (community), Wisconsin, an unincorporated community * Leroy Township, Calhoun County, Michigan * Leroy Township, Ingham County, Michigan * LeRoy Township, Lake County, Ohio * Leroy Township, Pennsylvania * LeRoy, West Virginia Elsewhere * Leroy, Saskatchewan, Canada * Rural Municipality of Leroy No. 339, Saskatchewan, Canada * 93102 Leroy, an asteroid Arts and entertainment * ''Leroy'' (film), a 2007 German comedy film * Leroy (''Lilo & Stitch''), a character in ''Leroy & Stitch'' * Leroy (''South Park''), a ''South Park'' character * "Leroy", a 1958 song by Jack Scott Other us ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Smn Theorem
In computability theory the ' theorem, (also called the translation lemma, parameter theorem, and the parameterization theorem) is a basic result about programming languages (and, more generally, Gödel numberings of the computable functions) (Soare 1987, Rogers 1967). It was first proved by Stephen Cole Kleene (1943). The name ' comes from the occurrence of an ''S'' with subscript ''n'' and superscript ''m'' in the original formulation of the theorem (see below). In practical terms, the theorem says that for a given programming language and positive integers ''m'' and ''n'', there exists a particular algorithm that accepts as input the source code of a program with free variables, together with ''m'' values. This algorithm generates source code that effectively substitutes the values for the first ''m'' free variables, leaving the rest of the variables free. Details The basic form of the theorem applies to functions of two arguments (Nies 2009, p. 6). Given a Gödel numbe ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
