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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),
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).
The measure NSPACE is used to define the complexity class whose solutions can be determined by a non-deterministic Turing machine.The complexity class NSPACE(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine, M, using space O(f(n)), where n is the length of the input.
In other words, if a nondeterministic Turing machine can solve a problem using () space, a deterministic Turing machine can solve the same problem in the square of that space bound. [1] Although it seems that nondeterminism may produce exponential gains in time (as formalized in the unproven exponential time hypothesis ), Savitch's theorem ...
In computational complexity theory, nondeterminism is often modeled using an explicit mechanism for making a nondeterministic choice, such as in a nondeterministic Turing machine. For these models, a nondeterministic algorithm is considered to perform correctly when, for each input, there exists a run that produces the desired result, even when ...
In computational complexity theory, the complexity class NTIME(f(n)) is the set of decision problems that can be solved by a non-deterministic Turing machine which runs in time O(f(n)). Here O is the big O notation, f is some function, and n is the size of the input (for which the problem is to be decided).
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 ...
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