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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.
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 FSM is defined by a list of its states, its initial state, and the inputs that trigger each transition. Finite-state machines are of two types—deterministic finite-state machines and non-deterministic finite-state machines. [2] For any non-deterministic finite-state machine, an equivalent deterministic one can be constructed.
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]
A deterministic algorithm is an algorithm which, given a particular input, will always produce the same output, with the underlying machine always passing through the same sequence of states. There may be non-deterministic algorithms that run on a deterministic machine, for example, an algorithm that relies on random choices.