Skip to content
EntityQ818888· pop 16· linked from 77 articles

computability

Sign in to save

Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.

~19 min read

Encyclopedic overview

14 sections
Contents
  • Problems
  • Power of automata
  • Power of finite-state machines
  • Power of pushdown automata
  • Power of Turing machines
  • The halting problem
  • Beyond recursively enumerable languages
  • Concurrency-based models
  • Stronger models of computation
  • Infinite execution
  • Oracle machines
  • Limits of hyper-computation
  • See also
  • References

Computability is the ability to solve a problem by an effective procedure. It is a key topic of the field of computability theory within mathematical logic and the theory of computation within computer science. The computability of a problem is closely linked to the existence of an algorithm to solve the problem.

The most widely studied models of computability are the Turing-computable and μ-recursive functions, and the lambda calculus, all of which have computationally equivalent power. Other forms of computability are studied as well: computability notions weaker than Turing machines are studied in automata theory, while computability notions stronger than Turing machines are studied in the field of hypercomputation.

Excerpted from Wikipedia’s “computability” article, available under the CC BY-SA 4.0 licence.