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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).
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]
He also saved the original interpreter and specification after the original site stopped functioning, and offered a general strategy of writing programs in Malbolge as well as some thoughts on its Turing completeness. [5] Olmstead believed Malbolge to be a linear bounded automaton. There's a discussion about whether one can implement sensible ...
As stated, the design goal for Befunge was to create a language which was difficult to compile. This was attempted with the implementation of self-modifying code (the 'p' instruction can write new instructions into the playfield) and a multi-dimensional playfield (the same instruction can be executed in four different directions).
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.
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]
FRACTRAN is a Turing-complete esoteric programming language invented by the mathematician John Conway. A FRACTRAN program is an ordered list of positive fractions together with an initial positive integer input n. The program is run by updating the integer n as follows: for the first fraction f in the list for which nf is an integer, replace n ...
In particular, the logic programming language Prolog is a Turing complete programming language. Datalog extends the relational database model with recursive relations, while answer set programming is a form of logic programming oriented towards difficult (primarily NP-hard) search problems.