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A nondeterministic Turing machine is a "parallel" Turing machine that can take many computational paths simultaneously, with the restriction that the parallel Turing machines ...

A problem is assigned to the NP (nondeterministic polynomial time) class if it is solvable in polynomial time by a nondeterministic Turing machine. A P-problem (whose ...

A problem is NP-hard if an algorithm for solving it can be translated into one for solving any NP-problem (nondeterministic polynomial time) problem. NP-hard therefore means ...

The theory of classifying problems based on how difficult they are to solve. A problem is assigned to the P-problem (polynomial-time) class if the number of steps needed to ...

A Turing machine is called deterministic if there is always at most one instruction associated with a given present internal state/tape state pair (q,s). Otherwise, it is ...

A problem which is both NP (verifiable in nondeterministic polynomial time) and NP-hard (any NP-problem can be translated into this problem). Examples of NP-hard problems ...

The Lucas-Lehmer test is an efficient deterministic primality test for determining if a Mersenne number M_n is prime. Since it is known that Mersenne numbers can only be ...

The Pratt certificate is a primality certificate based on Fermat's little theorem converse. Prior to the work of Pratt (1975), the Lucas-Lehmer test had been regarded purely ...

A Turing machine is a theoretical computing machine invented by Alan Turing (1937) to serve as an idealized model for mathematical calculation. A Turing machine consists of a ...