Blum's speedup theorem

Blum's speedup theorem

In computational complexity theory Blum's speedup theorem, first stated by Manuel Blum in 1967, is an important theorem about the complexity of computable functions.

Each computable function has an infinite number of different program representations in a given programming language. In the theory of algorithms one often needs to find the program with the smallest complexity for a given computable function and a given complexity measure. Blum's speedup theorem states that for any complexity measure there are computable functions which have no smallest program.

Speedup theorem

Given a Blum complexity measure (varphi, Phi) and a total computable function f with two parameters, then there exists a total computable predicate g (a boolean valued computable function) so that for every program i for g, there exists a program j for g so that for almost all x:f(x, Phi_j(x)) leq Phi_i(x)

f is called the speedup function.

See also

* speedup theorem

References

* M. Blum. "A machine-independent theory of the complexity of recursive functions". Journal of the ACM, 14, 322-336, 1967.

External links

*


Wikimedia Foundation. 2010.

Игры ⚽ Нужна курсовая?

Look at other dictionaries:

  • Speedup theorem — In computational complexity theory, a speedup theorem is a theorem that considers some algorithm solving a problem and demonstrates the existence of a faster algorithm solving the same problem (or more generally, an algorithm using less of any… …   Wikipedia

  • Speedup Theorem — In der Komplexitätstheorie dienen verschiedene Speedup Theoreme (Beschleunigungssätze) für den Nachweis, dass eine Maschine oder ein Algorithmus um einen gewissen Faktor beschleunigt werden kann, wenn bereits eine andere Maschine oder ein anderer …   Deutsch Wikipedia

  • Speedup-Theorem — In der Komplexitätstheorie dienen verschiedene Speedup Theoreme (Beschleunigungssätze) für den Nachweis, dass eine Maschine oder ein Algorithmus um einen gewissen Faktor beschleunigt werden kann, wenn bereits eine andere Maschine oder ein anderer …   Deutsch Wikipedia

  • Blum — Blume means flower in German. In English, the name Blum can either be pronounced /blʌm/, /blu:m/ or /blum/.People*Brad Blum CEO of Burger King from 2002 until 2004. *Geoff Blum baseball player *H Steven Blum three star general of the United… …   Wikipedia

  • Manuel Blum — Born April 26, 1938 (1938 04 26) (age 73) Caracas, Venezuela Residence Pittsburgh …   Wikipedia

  • Gap theorem — See also Gap theorem (disambiguation) for other gap theorems in mathematics. In computational complexity theory the Gap theorem is a major theorem about the complexity of computable functions. [Lance Fortnow, Steve Homer,… …   Wikipedia

  • Manuel Blum — (* 26. April 1938 in Caracas, Venezuela) ist ein venezolanischer Informatiker, der 1995 „in Anerkennung seiner Beiträge zu den Grundlagen der algorithmischen Komplexitätstheorie sowie deren Anwendung in der Kryptographie und der Fehlerüberprüfung …   Deutsch Wikipedia

  • Asymptotically optimal — In computer science, an algorithm is said to be asymptotically optimal if, roughly speaking, for large inputs it performs at worst a constant factor (independent of the input size) worse than the best possible algorithm. It is a term commonly… …   Wikipedia

  • Komplexitätstheorie — Die Komplexitätstheorie als Teilgebiet der Theoretischen Informatik befasst sich mit der Komplexität von algorithmisch behandelbaren Problemen auf verschiedenen mathematisch definierten formalen Rechnermodellen. Die Komplexität von Algorithmen… …   Deutsch Wikipedia

  • Space-time tradeoff — In computer science, a space time or time memory tradeoff is a situation where the memory use can be reduced at the cost of slower program execution, or vice versa, the computation time can be reduced at the cost of increased memory use. As the… …   Wikipedia

Share the article and excerpts

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