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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),
and a deterministic polynomial-time Turing machine is a deterministic Turing machine M that satisfies two conditions: M halts on all inputs w and there exists k ∈ N {\displaystyle k\in N} such that T M ( n ) ∈ O ( n k ) {\displaystyle T_{M}(n)\in O(n^{k})} , where O refers to the big O notation and
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).
Turing machines with input-and-output also have the same time complexity as other Turing machines; in the words of Papadimitriou 1994 Prop 2.2: For any k -string Turing machine M operating within time bound f ( n ) {\displaystyle f(n)} there is a ( k + 2 ) {\displaystyle (k+2)} -string Turing machine M' with input and output ...
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]
In computer science, a universal Turing machine (UTM) is a Turing machine capable of computing any computable sequence, [1] as described by Alan Turing in his seminal paper "On Computable Numbers, with an Application to the Entscheidungsproblem". Common sense might say that a universal machine is impossible, but Turing proves that it is possible.
A deterministic Turing machine is the most basic Turing machine, which uses a fixed set of rules to determine its future actions. A probabilistic Turing machine is a deterministic Turing machine with an extra supply of random bits. The ability to make probabilistic decisions often helps algorithms solve problems more efficiently.
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 ...