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In computability theory, a system of data-manipulation rules (such as a model of computation, a computer's instruction set, a programming language, or a cellular automaton) is said to be Turing-complete or computationally universal if it can be used to simulate any Turing machine [1] [2] (devised by English mathematician and computer scientist Alan Turing).
Among the 88 possible unique elementary cellular automata, Rule 110 is the only one for which Turing completeness has been directly proven, although proofs for several similar rules follow as simple corollaries (e.g. Rule 124, which is the horizontal reflection of Rule 110). Rule 110 is arguably the simplest known Turing complete system. [2] [5]
Turing is a high-level, general purpose programming language developed in 1982 by Ric Holt and James Cordy, at University of Toronto in Ontario, Canada. It was designed to help students taking their first computer science course learn how to code.
Turing completeness is the ability for a computational model or a system of instructions to simulate a Turing machine. A programming language that is Turing complete is theoretically capable of expressing all tasks accomplishable by computers; nearly all programming languages are Turing complete if the limitations of finite memory are ignored.
PostScript is a Turing-complete programming language, belonging to the concatenative group of programming languages. It is an interpreted, stack-based language similar to Forth but with strong dynamic typing, data structures inspired by those found in Lisp, scoped memory and, since language level 2, garbage collection.
TeX82 also uses fixed-point arithmetic instead of floating-point, to ensure reproducibility of the results across different computer hardware, [9] and includes a real, Turing-complete programming language, following intense lobbying by Guy Steele. [10] In 1989, Donald Knuth released new versions of TeX and Metafont. [11]
If an NL-complete language X could belong to L, then so would every other language Y in NL.For, suppose (by NL-completeness) that there existed a deterministic logspace reduction r that maps an instance y of problem Y to an instance x of problem X, and also (by the assumption that X is in L) that there exists a deterministic logspace algorithm A for solving problem X.
54. Beware of the Turing tar-pit in which everything is possible but nothing of interest is easy. In any Turing complete language, it is possible to write any computer program, so in a very rigorous sense nearly all programming languages are equally capable. However, having that theoretical ability is not the same as usefulness in practice.