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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 other runs produce incorrect results. This existential power makes nondeterministic algorithms of this sort more efficient than known deterministic algorithms for many problems.
Comparison of deterministic and nondeterministic computation. In contrast to a deterministic Turing machine, in a nondeterministic Turing machine (NTM) the set of rules may prescribe more than one action to be performed for any given situation. For example, an X on the tape in state 3 might allow the NTM to:
Deterministic algorithms are by far the most studied and familiar kind of algorithm, as well as one of the most practical, since they can be run on real machines efficiently. Formally, a deterministic algorithm computes a mathematical function ; a function has a unique value for any input in its domain , and the algorithm is a process that ...
Regular languages are a category of languages (sometimes termed Chomsky Type 3) which can be matched by a state machine (more specifically, by a deterministic finite automaton or a nondeterministic finite automaton) constructed from a regular expression. In particular, a regular language can match constructs like "A follows B", "Either A or B ...
These two definitions are equivalent because the algorithm based on the Turing machine consists of two phases, the first of which consists of a guess about the solution, which is generated in a nondeterministic way, while the second phase consists of a deterministic algorithm that verifies whether the guess is a solution to the problem. [3]
A comparison of deterministic and nondeterministic computation. If any branch on the nondeterministic computation accepts then the NTM accepts. The deterministic Turing machine (DTM) is a variant of the nondeterministic Turing machine (NTM).
In computational complexity theory, the space hierarchy theorems are separation results that show that both deterministic and nondeterministic machines can solve more problems in (asymptotically) more space, subject to certain conditions. For example, a deterministic Turing machine can solve more decision problems in space n log n than in space n.
In computer science, Thompson's construction algorithm, also called the McNaughton–Yamada–Thompson algorithm, [1] is a method of transforming a regular expression into an equivalent nondeterministic finite automaton (NFA). [2] This NFA can be used to match strings against the regular expression. This algorithm is credited to Ken Thompson.