recursive and recursively enumerable sets

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• Recursively enumerable set — In computability theory, traditionally called recursion theory, a set S of natural numbers is called recursively enumerable, computably enumerable, semidecidable, provable or Turing recognizable if: There is an algorithm such that the set of… …   Wikipedia

• Recursive set — In computability theory, a set of natural numbers is called recursive, computable or decidable if there is an algorithm which terminates after a finite amount of time and correctly decides whether or not a given number belongs to the set. A more… …   Wikipedia

• Recursive languages and sets — This article is a temporary experiment to see whether it is feasible and desirable to merge the articles Recursive set, Recursive language, Decidable language, Decidable problem and Undecidable problem. Input on how best to do this is very much… …   Wikipedia

• Creative and productive sets — In computability theory, productive sets and creative sets are types of sets of natural numbers that have important applications in mathematical logic. They are a standard topic in mathematical logic textbooks such as Soare (1987) and Rogers… …   Wikipedia

• Μ-recursive function — In mathematical logic and computer science, the μ recursive functions are a class of partial functions from natural numbers to natural numbers which are computable in an intuitive sense. In fact, in computability theory it is shown that the μ… …   Wikipedia

• Primitive recursive function — The primitive recursive functions are defined using primitive recursion and composition as central operations and are a strict subset of the recursive functions (recursive functions are also known as computable functions). The term was coined by… …   Wikipedia

• Limiting recursive — In computability theory, the term limiting recursive (also limit recursive or limit computable) describes sets that are the limit of a sequence of computable sets. Definition A set S is limiting recursive if there is a total computable function g …   Wikipedia

• μ-recursive function — In mathematical logic and computer science, the μ recursive functions are a class of partial functions from natural numbers to natural numbers which are computable in an intuitive sense. In fact, in computability theory it is shown that the μ… …   Wikipedia

• Recursion theory — Recursion theory, also called computability theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown to include the study of generalized computability… …   Wikipedia

• Computability theory — For the concept of computability, see Computability. Computability theory, also called recursion theory, is a branch of mathematical logic that originated in the 1930s with the study of computable functions and Turing degrees. The field has grown …   Wikipedia

• automata theory — Body of physical and logical principles underlying the operation of any electromechanical device (an automaton) that converts information input in one form into another, or into some action, according to an algorithm. Norbert Wiener and Alan M.… …   Universalium