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Classes of automata. (Clicking on each layer gets an article on that subject) A Turing machine is a mathematical model of computation describing an abstract machine [ 1 ] that manipulates symbols on a strip of tape according to a table of rules. [ 2 ] Despite the model's simplicity, it is capable of implementing any computer algorithm.
The Automatic Computing Engine (ACE) was a British early electronic serial stored-program computer design by Alan Turing. Turing completed the ambitious design in late 1945, having had experience in the years prior with the secret Colossus computer at Bletchley Park. The ACE was not built, but a smaller version, the Pilot ACE, was constructed ...
Alan Mathison Turing OBE FRS (/ ˈtjʊərɪŋ /; 23 June 1912 – 7 June 1954) was an English mathematician, computer scientist, logician, cryptanalyst, philosopher and theoretical biologist. [ 5 ] He was highly influential in the development of theoretical computer science, providing a formalisation of the concepts of algorithm and computation ...
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
Turing completeness is used as a way to express the power of such a data-manipulation rule set. Virtually all programming languages today are Turing-complete. [ a ] A related concept is that of Turing equivalence – two computers P and Q are called equivalent if P can simulate Q and Q can simulate P. [citation needed] The Church–Turing ...
e. In theoretical computer science, a nondeterministic Turing machine (NTM) is a theoretical model of computation whose governing rules specify more than one possible action when in some given situations. That is, an NTM's next state is not completely determined by its action and the current symbol it sees, unlike a deterministic Turing machine.
To attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are problems that any other NP problem is reducible to in polynomial time and whose solution is still verifiable in polynomial time. That is, any NP problem can be transformed into any NP-complete problem. Informally, an NP-complete problem is an ...
Halting problem. hide. In computability theory, the halting problem is the problem of determining, from a description of an arbitrary computer program and an input, whether the program will finish running, or continue to run forever. The halting problem is undecidable, meaning that no general algorithm exists that solves the halting problem for ...