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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.
A nondeterministic programming language is a language which can specify, at certain points in the program (called "choice points"), various alternatives for program flow. Unlike an if-then statement , the method of choice between these alternatives is not directly specified by the programmer; the program must decide at run time between the ...
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]
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: Write a Y, move right, and switch to ...
The obtained automaton is non-deterministic, and it has as many states as the number of letters of the regular expression, plus one. Furthermore, it has been shown [ 3 ] : 215 [ 4 ] that Glushkov's automaton is the same as Thompson's automaton when the ε-transitions are removed.
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.
The set of all strings accepted by an NFA is the language the NFA accepts. This language is a regular language. For every NFA a deterministic finite automaton (DFA) can be found that accepts the same language. Therefore, it is possible to convert an existing NFA into a DFA for the purpose of implementing a (perhaps) simpler machine.
This is a polynomial-time algorithm accepting an NP-complete language only if P = NP. "Accepting" means it gives "yes" answers in polynomial time, but is allowed to run forever when the answer is "no" (also known as a semi-algorithm). This algorithm is enormously impractical, even if P = NP.