FP (complexity)

FP (complexity)

In computational complexity theory, the complexity class FP is the set of function problems which can be solved by a deterministic Turing machine in polynomial time; it is the function problem version of the decision problem class P. Roughly speaking, it is the class of functions that can be efficiently computed on classical computers without randomization.

FP is formally defined as:

:A binary relation P("x","y") is in FP if and only if there is a deterministic polynomial time algorithm that, given "x", can find some "y" such that P("x","y") holds.

The difference between FP and P is that problems in P have one-bit, yes/no answers, while problems in FP can have any output that can be computed in polynomial time. For example, adding two numbers is an FP problem, while determining if their sum is odd is in P. More complex is the relationship between FP and FNP. FNP is defined as follows:

:A binary relation P("x","y"), where "y" is at most polynomially longer than "x", is in FNP if and only if there is a deterministic polynomial time algorithm that can determine whether P("x","y") holds given both "x" and "y".

That is, instead of merely verifying "y", the algorithm for solving an FP problem must find its value. This is similar to the computation/verification relationship between P and NP; it also shows that FP is contained in FNP. In fact, FP = FNP if and only if P = NP.

Polynomial-time function problems are fundamental in defining polynomial-time reductions, which are used in turn to define the class of NP-complete problems.

Because a machine that uses logarithmic space has at most polynomially many configurations, FL, the set of function problems which can be calculated in logspace, is contained in FP. It is not known whether FL = FP; this is analogous to the problem of determining whether the decision classes P and L are equal.

References

* [http://qwiki.stanford.edu/wiki/Complexity_Zoo:F#fp Complexity Zoo: FP]


Wikimedia Foundation. 2010.

Игры ⚽ Нужно решить контрольную?

Look at other dictionaries:

  • Complexity management — is a business methodology that deals with the analysis and optimization of complexity in enterprises. Effects of complexity pertain to all business processes along the value chain and hence complexity management requires a holistic approach.… …   Wikipedia

  • Complexity theory and organizations — Complexity theory and organizations, also called complexity strategy or complex adaptive organization, is the use of Complexity theory in the field of strategic management and organizational studies. Contents 1 Overview 2 Early research 3 Later… …   Wikipedia

  • compLexity — coL Логотип организации Страна …   Википедия

  • Complexity theory and strategy — Complexity theory has been used extensively in the field of strategic management and organizational studies, sometimes called complexity strategy or complex adaptive organization on the internet or in popular press. Broadly speaking, complexity… …   Wikipedia

  • Complexity (journal) —   Discipline Complex Systems …   Wikipedia

  • Complexity, Problem Solving, and Sustainable Societies — is a paper on energy economics by Joseph Tainter from 1996. Contents 1 Focus 1.1 Attempts 1.2 Requirement of knowledge 2 See …   Wikipedia

  • Complexity theory — may refer to: The study of a complex system or complex systems Complexity theory and organizations, the application of complexity theory to strategy Complexity economics, the application of complexity theory to economics Chaos theory, the study… …   Wikipedia

  • compLexity — Kürzel coL Manager Vereinigte Staaten Jason „1“ Lake …   Deutsch Wikipedia

  • Complexity — Com*plex i*ty, n.; pl. {Complexities}. [Cf. F. complexit[ e].] 1. The state of being complex; intricacy; entanglement. [1913 Webster] The objects of society are of the greatest possible complexity. Burke. [1913 Webster] 2. That which is complex;… …   The Collaborative International Dictionary of English

  • complexity — complexity. См. сложность генома. (Источник: «Англо русский толковый словарь генетических терминов». Арефьев В.А., Лисовенко Л.А., Москва: Изд во ВНИРО, 1995 г.) …   Молекулярная биология и генетика. Толковый словарь.

  • complexity — index complication, confusion (turmoil), enigma, entanglement (confusion), imbroglio, impasse …   Law dictionary

Share the article and excerpts

Direct link
Do a right-click on the link above
and select “Copy Link”