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Turing Machine Equivalents
A Turing machine is a hypothetical computing device, first conceived by Alan Turing in 1936. Turing machines manipulate symbols on a potentially infinite strip of tape according to a finite table of rules, and they provide the theoretical underpinnings for the notion of a computer algorithm. While none of the following models have been shown to have more power than the single-tape, one-way infinite, multi-symbol Turing-machine model, their authors defined and used them to investigate questions and solve problems more easily than they could have if they had stayed with Turing's ''a''-machine model. Machines equivalent to the Turing machine model Turing equivalence Many machines that might be thought to have more computational capability than a simple universal Turing machine can be shown to have no more power. They might compute faster, perhaps, or use less memory, or their instruction set might be smaller, but they cannot compute more powerfully (i.e. more mathematical funct ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Turing Machine
A Turing machine is a mathematical model of computation describing an abstract machine that manipulates symbols on a strip of tape according to a table of rules. Despite the model's simplicity, it is capable of implementing any computer algorithm. The machine operates on an infinite memory tape divided into discrete mathematics, discrete cells, each of which can hold a single symbol drawn from a finite set of symbols called the Alphabet (formal languages), alphabet of the machine. It has a "head" that, at any point in the machine's operation, is positioned over one of these cells, and a "state" selected from a finite set of states. At each step of its operation, the head reads the symbol in its cell. Then, based on the symbol and the machine's own present state, the machine writes a symbol into the same cell, and moves the head one step to the left or the right, or halts the computation. The choice of which replacement symbol to write, which direction to move the head, and whet ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Cook–Levin Theorem
In computational complexity theory, the Cook–Levin theorem, also known as Cook's theorem, states that the Boolean satisfiability problem is NP-completeness, NP-complete. That is, it is in NP (complexity), NP, and any problem in NP can be reduction (complexity), reduced in polynomial time by a deterministic Turing machine to the Boolean satisfiability problem. The theorem is named after Stephen Cook and Leonid Levin. The proof is due to Richard Karp, based on an earlier proof (using a different notion of reducibility) by Cook. An important consequence of this theorem is that if there exists a deterministic polynomial-time algorithm for solving Boolean satisfiability, then every NP (complexity), NP problem can be solved by a deterministic polynomial-time algorithm. The question of whether such an algorithm for Boolean satisfiability exists is thus equivalent to the P versus NP problem, which is still widely considered the most important unsolved problem in theoretical computer sc ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Space Complexity
The space complexity of an algorithm or a data structure is the amount of memory space required to solve an instance of the computational problem as a function of characteristics of the input. It is the memory required by an algorithm until it executes completely. This includes the memory space used by its inputs, called input space, and any other (auxiliary) memory it uses during execution, which is called auxiliary space. Similar to time complexity, space complexity is often expressed asymptotically in big ''O'' notation, such as O(n), O(n\log n), O(n^\alpha), O(2^n), etc., where is a characteristic of the input influencing space complexity. Space complexity classes Analogously to time complexity classes DTIME(f(n)) and NTIME(f(n)), the complexity classes DSPACE(f(n)) and NSPACE(f(n)) are the sets of languages that are decidable by deterministic (respectively, non-deterministic) Turing machines that use O(f(n)) space. The complexity classes PSPACE and NPSPACE allow f to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Sublinear
In linear algebra, a sublinear function (or functional as is more often used in functional analysis), also called a quasi-seminorm or a Banach functional, on a vector space X is a real-valued function with only some of the properties of a seminorm. Unlike seminorms, a sublinear function does not have to be nonnegative-valued and also does not have to be absolutely homogeneous. Seminorms are themselves abstractions of the more well known notion of norms, where a seminorm has all the defining properties of a norm that it is not required to map non-zero vectors to non-zero values. In functional analysis the name Banach functional is sometimes used, reflecting that they are most commonly used when applying a general formulation of the Hahn–Banach theorem. The notion of a sublinear function was introduced by Stefan Banach when he proved his version of the Hahn-Banach theorem. There is also a different notion in computer science, described below, that also goes by the name "su ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Pointer Machine
In theoretical computer science, a pointer machine is an atomistic abstract computational machine whose storage structure is a graph. A pointer algorithm could also be an algorithm restricted to the pointer machine model. Some particular types of pointer machines are called a linking automaton, a KU-machine, an SMM, an atomistic LISP machine, a tree-pointer machine, etc. Amir Ben-Amram (1995). What is a "Pointer machine"?, SIGACT News (ACM Special Interest Group on Automata and Computability Theory), volume 26, 1995. Pointer machines do not have arithmetic instructions. Computation proceeds only by reading input symbols, modifying and doing various tests on its storage structure—the pattern of nodes and pointers, and outputting symbols based on the tests. In this sense, the model is similar to the Turing machine. Types of "pointer machines" Both Gurevich and Ben-Amram list a number of very similar "atomistic" models of "abstract machines"; Yuri Gurevich (2000), ''Sequential ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Abraham Robinson
Abraham Robinson (born Robinsohn; October 6, 1918 – April 11, 1974) was a mathematician who is most widely known for development of nonstandard analysis, a mathematically rigorous system whereby infinitesimal and infinite numbers were reincorporated into modern mathematics. Nearly half of Robinson's papers were in applied mathematics rather than in pure mathematics. Biography He was born to a Jewish family with strong Zionist beliefs, in Waldenburg, Germany, which is now Wałbrzych, in Poland. In 1933, he immigrated to British Mandate of Palestine, where he earned a first degree from the Hebrew University. Robinson was in France when the Nazis invaded during World War II, and escaped by train and on foot, being alternately questioned by French soldiers suspicious of his German passport and asked by them to share his map, which was more detailed than theirs. While in London, he joined the Free French Air Force and contributed to the war effort by teaching himself aerodynam ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Calvin Elgot
Calvin may refer to: Names * Calvin (given name) ** Particularly Calvin Coolidge, 30th President of the United States * Calvin (surname) ** Particularly John Calvin, theologian Places In the United States * Calvin, Arkansas, a hamlet * Calvin Township, Jewell County, Kansas * Calvin, Louisiana, a village * Calvin Township, Michigan ** Calvin crater, an impact crater * Calvin, North Dakota, a city * Calvin, Oklahoma, a town * Calvin, Virginia * Calvin, West Virginia, an unincorporated community Elsewhere * Calvin, Ontario, Canada, a township * Mount Calvin, Victoria Land, Antarctica Schools * Calvin University (South Korea), a Presbyterian-affiliated university in South Korea * Calvin University, Grand Rapids, Michigan * Calvin Theological Seminary, Grand Rapids, Michigan * Calvin High School (other), various American schools * Calvin Christian School (Escondido, California) * Calvin Christian School (Kingston, Tasmania) * Collège Calvin, the oldest pub ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Stephen Cook
Stephen Arthur Cook (born December 14, 1939) is an American-Canadian computer scientist and mathematician who has made significant contributions to the fields of complexity theory and proof complexity. He is a university professor emeritus at the University of Toronto, Department of Computer Science and Department of Mathematics. He is considered one of the forefathers of computational complexity theory. Biography Cook received his bachelor's degree in 1961 from the University of Michigan, and his master's degree and PhD from Harvard University, respectively in 1962 and 1966, from the Mathematics Department. He joined the University of California, Berkeley, mathematics department in 1966 as an assistant professor, and stayed there until 1970 when he was denied reappointment. In a speech celebrating the 30th anniversary of the Berkeley electrical engineering and computer sciences department, fellow Turing Award winner and Berkeley professor Richard Karp said that, "It is to ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Von Neumann Architecture
The von Neumann architecture—also known as the von Neumann model or Princeton architecture—is a computer architecture based on the '' First Draft of a Report on the EDVAC'', written by John von Neumann in 1945, describing designs discussed with John Mauchly and J. Presper Eckert at the University of Pennsylvania's Moore School of Electrical Engineering. The document describes a design architecture for an electronic digital computer made of "organs" that were later understood to have these components: * A processing unit with both an arithmetic logic unit and processor registers * A control unit that includes an instruction register and a program counter * Memory that stores data and instructions * External mass storage * Input and output mechanisms.. The attribution of the invention of the architecture to von Neumann is controversial, not least because Eckert and Mauchly had done a lot of the required design work and claim to have had the idea for stored programs ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Marvin Minsky
Marvin Lee Minsky (August 9, 1927 – January 24, 2016) was an American cognitive scientist, cognitive and computer scientist concerned largely with research in artificial intelligence (AI). He co-founded the Massachusetts Institute of Technology's AI laboratory and wrote extensively about AI and philosophy. Minsky received many accolades and honors, including the 1969 Turing Award. Early life and education Marvin Lee Minsky was born in New York City, to Henry, an eye surgeon, and Fannie (Reiser), a Zionism, Zionist activist. His family was Jewish. He attended the Ethical Culture Fieldston School and the Bronx High School of Science. He later attended Phillips Academy in Andover, Massachusetts, Andover, Massachusetts. He then served in the United States Navy, US Navy from 1944 to 1945. He received a B.A. in mathematics from Harvard University in 1950 and a Doctor of Philosophy, Ph.D. in mathematics from Princeton University in 1954. His doctoral dissertation was titled "Theory of ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
μ Recursion
In mathematical logic and computer science, a general recursive function, partial recursive function, or μ-recursive function is a partial function from natural numbers to natural numbers that is "computable" in an intuitive sense – as well as in a formal one. If the function is total, it is also called a total recursive function (sometimes shortened to recursive function). In computability theory, it is shown that the μ-recursive functions are precisely the functions that can be computed by Turing machines (this is one of the theorems that supports the Church–Turing thesis). The μ-recursive functions are closely related to primitive recursive functions, and their inductive definition (below) builds upon that of the primitive recursive functions. However, not every total recursive function is a primitive recursive function—the most famous example is the Ackermann function. Other equivalent classes of functions are the functions of lambda calculus and the functions tha ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Recursion (computer Science)
In computer science, recursion is a method of solving a computational problem where the solution depends on solutions to smaller instances of the same problem. Recursion solves such recursion, recursive problems by using function (computer science), functions that call themselves from within their own code. The approach can be applied to many types of problems, and recursion is one of the central ideas of computer science. Most computer programming languages support recursion by allowing a function to call itself from within its own code. Some functional programming languages (for instance, Clojure) do not define any looping constructs but rely solely on recursion to repeatedly call code. It is proved in computability theory that these recursive-only languages are Turing complete; this means that they are as powerful (they can be used to solve the same problems) as imperative languages based on control structures such as and . Repeatedly calling a function from within itse ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
