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A deterministic Turing machine has a transition function that, for a given state and symbol under the tape head, specifies three things: the symbol to be written to the tape (it may be the same as the symbol currently in that position, or not even write at all, resulting in no practical change),
NP is the set of decision problems for which the problem instances, where the answer is "yes", have proofs verifiable in polynomial time by a deterministic Turing machine, or alternatively the set of problems that can be solved in polynomial time by a nondeterministic Turing machine. [2][Note 1] NP is the set of decision problems solvable in ...
NEXPTIME. In computational complexity theory, the complexity class NEXPTIME (sometimes called NEXP) is the set of decision problems that can be solved by a non-deterministic Turing machine using time . In terms of NTIME, Alternatively, NEXPTIME can be defined using deterministic Turing machines as verifiers. A language L is in NEXPTIME if and ...
Nondeterministic algorithm. In computer science and computer programming, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. Different models of computation give rise to different reasons that an algorithm may be non ...
An oracle machine or o-machine is a Turing a-machine that pauses its computation at state "o" while, to complete its calculation, it "awaits the decision" of "the oracle"—an entity unspecified by Turing "apart from saying that it cannot be a machine" (Turing (1939), The Undecidable, p. 166–168).
An alternating Turing machine (or to be more precise, the definition of acceptance for such a machine) alternates between these modes. An alternating Turing machine is a non-deterministic Turing machine whose states are divided into two sets: existential states and universal states. An existential state is accepting if some transition leads to ...
Class of computational decision problems for which any given yes -solution can be verified as a solution in polynomial time by a deterministic Turing machine (or solvable by a non-deterministic Turing machine in polynomial time). NP-hard. Class of problems which are at least as hard as the hardest problems in NP.
To attack the P = NP question, the concept of NP-completeness is very useful. NP-complete problems are problems that any other NP problem is reducible to in polynomial time and whose solution is still verifiable in polynomial time. That is, any NP problem can be transformed into any NP-complete problem. Informally, an NP-complete problem is an ...