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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]
Counter machines with two counters are Turing complete: they can simulate any appropriately-encoded Turing machine, but there are some simple functions that they cannot compute. Counter machines with only a single counter can recognize a proper superset of the regular languages and a subset of the deterministic context free languages .
Although Horn clause logic programs are Turing complete, [1] [2] for most practical applications, Horn clause programs need to be extended to "normal" logic programs with negative conditions. For example, the definition of sibling uses a negative condition, where the predicate = is defined by the clause X = X :
Among other things, he developed a proof showing that the Rule 110 cellular automaton is Turing-complete. Cook presented his proof at the Santa Fe Institute conference CA98 before the publishing of Wolfram's book—an action that led Wolfram Research to accuse Cook of violating his NDA and resulted in the blocking of the publication of the ...
The concept of NP-completeness was developed in the late 1960s and early 1970s in parallel by researchers in North America and the Soviet Union.In 1971, Stephen Cook published his paper "The complexity of theorem proving procedures" [2] in conference proceedings of the newly founded ACM Symposium on Theory of Computing.
From January 2008 to January 2011, if you bought shares in companies when Richard D. DiCerchio joined the board, and sold them when he left, you would have a 4.1 percent return on your investment, compared to a -13.4 percent return from the S&P 500.
Arithmetic-based Turing-complete machines use an arithmetic operation and a conditional jump. Like the two previous universal computers, this class is also Turing-complete. The instruction operates on integers which may also be addresses in memory. Currently there are several known OISCs of this class, based on different arithmetic operations: