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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 ...
When the cost denotes the running time of an algorithm, Yao's principle states that the best possible running time of a deterministic algorithm, on a hard input distribution, gives a lower bound for the expected time of any Las Vegas algorithm on its worst-case input. Here, a Las Vegas algorithm is a randomized algorithm whose runtime may vary ...
The NIST Dictionary of Algorithms and Data Structures [1] is a reference work maintained by the U.S. National Institute of Standards and Technology. It defines a large number of terms relating to algorithms and data structures. For algorithms and data structures not necessarily mentioned here, see list of algorithms and list of data structures.
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.
Flowchart of using successive subtractions to find the greatest common divisor of number r and s. In mathematics and computer science, an algorithm (/ ˈ æ l ɡ ə r ɪ ð əm / ⓘ) is a finite sequence of mathematically rigorous instructions, typically used to solve a class of specific problems or to perform a computation. [1]
If an NL-complete language X could belong to L, then so would every other language Y in NL.For, suppose (by NL-completeness) that there existed a deterministic logspace reduction r that maps an instance y of problem Y to an instance x of problem X, and also (by the assumption that X is in L) that there exists a deterministic logspace algorithm A for solving problem X.
In this case, the algorithm returns true when the machine has a nondeterministic accepting path, and false otherwise. The number of configurations in this graph is (()), from which it follows that applying the algorithm to this implicit graph uses space (()). Thus by deciding connectivity in a graph representing nondeterministic Turing machine ...
The algorithm, as Deutsch had originally proposed it, was not deterministic. The algorithm was successful with a probability of one half. In 1992, Deutsch and Jozsa produced a deterministic algorithm which was generalized to a function which takes bits for its input. Unlike Deutsch's algorithm, this algorithm required two function evaluations ...