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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 ...
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 ...
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]
An algorithm is fundamentally a set of rules or defined procedures that is typically designed and used to solve a specific problem or a broad set of problems.. Broadly, algorithms define process(es), sets of rules, or methodologies that are to be followed in calculations, data processing, data mining, pattern recognition, automated reasoning or other problem-solving operations.
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 ...
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 ...