Nondeterministic algorithm

In computer science, a nondeterministic algorithm is an algorithm that, even for the same input, can exhibit different behaviors on different runs, as opposed to a deterministic algorithm. There are several ways an algorithm may behave differently from run to run. A concurrent algorithm can perform differently on different runs due to a race condition. A probabilistic algorithm's behaviors depends on a random number generator. An algorithm that solves a problem in nondeterministic polynomial time can run in polynomial time or exponential time depending on the choices it makes during execution. The nondeterministic algorithms are often used to find an approximation to a solution, when the exact solution would be too costly to obtain using a deterministic one.

The notion was introduced by Robert W. Floyd.

Often in computational theory, the term "algorithm" refers to a deterministic algorithm. A nondeterministic algorithm is different from its more familiar deterministic counterpart in its ability to arrive at outcomes using various routes. If a deterministic algorithm represents a single path from an input to an outcome, a nondeterministic algorithm represents a single path stemming into many paths, some of which may arrive at the same output and some of which may arrive at unique outputs. This property is captured mathematically in "nondeterministic" models of computation such as the nondeterministic finite automaton. In some scenarios, all possible paths are allowed to run simultaneously.

In algorithm design, nondeterministic algorithms are often used when the problem solved by the algorithm inherently allows multiple outcomes (or when there is a single outcome with multiple paths by which the outcome may be discovered, each equally preferable). Crucially, every outcome the nondeterministic algorithm produces is valid, regardless of which choices the algorithm makes while running.

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