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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).
The termination analysis is even more difficult than the Halting problem: the termination analysis in the model of Turing machines as the model of programs implementing computable functions would have the goal of deciding whether a given Turing machine is a total Turing machine, and this problem is at level of the arithmetical hierarchy and ...
A Turing machine is an idealised model of a central processing unit (CPU) that controls all data manipulation done by a computer, with the canonical machine using sequential memory to store data. Typically, the sequential memory is represented as a tape of infinite length on which the machine can perform read and write operations.
Python is a high-level, general-purpose programming language. Its design philosophy emphasizes code readability with the use of significant indentation. [33] Python is dynamically type-checked and garbage-collected. It supports multiple programming paradigms, including structured (particularly procedural), object-oriented and functional ...
Turing+ (Turing Plus) is a concurrent systems programming language based on the Turing programming language designed by James Cordy and Ric Holt, then at the University of Toronto, Canada, in 1987. Some, but not all, of the features of Turing+ were eventually subsumed into Object-Oriented 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]
The most common number-manipulation schemes—both in formal mathematics and in routine life—are: (1) the recursive functions calculated by a person with paper and pencil, and (2) the Turing machine or its Turing equivalents—the primitive register-machine or "counter-machine" model, the random-access machine model (RAM), the random-access ...
A recipient of the Turing award, [3] he is considered one of the greatest computer programmers of all time. [ 4 ] [ 5 ] [ 6 ] Other notable contributions included his work on regular expressions and early computer text editors QED and ed , the definition of the UTF-8 encoding, and his work on computer chess that included the creation of endgame ...