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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),
Common equivalent models are the multi-tape Turing machine, multi-track Turing machine, machines with input and output, and the non-deterministic Turing machine (NDTM) as opposed to the deterministic Turing machine (DTM) for which the action table has at most one entry for each combination of symbol and state.
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 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 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 ...
A probabilistic Turing machine is similar to a deterministic Turing machine, except rather than following a single transition function (a set of rules for how to proceed at each step of the computation) it probabilistically selects between multiple transition functions at each step.
An LBA differs from a Turing machine in that while the tape is initially considered to have unbounded length, only a finite contiguous portion of the tape, whose length is a linear function of the length of the initial input, can be accessed by the read/write head; hence the name linear bounded automaton. [1]: 225