In mathematics, logic and computer science, a formal language is called recursively enumerable (also recognizable, partially decidable, semidecidable, Turing-acceptable or Turing-recognizable) if it is a recursively enumerable subset in the set of all possible words over the alphabet of the language, i.e., if there exists a Turing machine which will enumerate all valid strings of the language.
Recursively enumerable languages are known as type-0 languages in the Chomsky hierarchy of formal languages. All regular, context-free, context-sensitive and recursive languages are recursively enumerable.
The class of all recursively enumerable languages is called RE.
and 23 Related for: Recursively enumerable language information
enumerable languages is called RE. There are three equivalent definitions of a recursivelyenumerablelanguage: A recursivelyenumerablelanguage is a recursively...
theory, a set S of natural numbers is called computably enumerable (c.e.), recursivelyenumerable (r.e.), semidecidable, partially decidable, listable,...
This type of language was not defined in the Chomsky hierarchy of (Chomsky 1959). All recursivelanguages are also recursivelyenumerable. All regular...
recursively enumerable, but not recursive? And, furthermore, are there languages which are not even recursivelyenumerable? The halting problem is one of...
Recursivelyenumerablelanguages are closed under Kleene star, concatenation, union, and intersection, but not under set difference; see Recursively enumerable...
nondecreasing total computable function is computable. RecursivelyenumerablelanguageRecursivelanguage Recursion Cutland, N. Computability. Cambridge University...
context-free language is context-sensitive, every context-sensitive language is recursive and every recursivelanguage is recursivelyenumerable. These are...
context-free languages and the recursivelyenumerablelanguages, and other families of formal languages studied in the scientific literature. A formal language is...
context free languages can be any recursivelyenumerablelanguage. The quotient of two recursivelyenumerablelanguages is recursivelyenumerable. These closure...
computable. The set being enumerated is then called recursivelyenumerable (or computably enumerable in more contemporary language), referring to the use...
machine can calculate any recursive function, decide any recursivelanguage, and accept any recursivelyenumerablelanguage. According to the Church–Turing...
call a subset U of FS recursive (respectively recursivelyenumerable) if f(U) is recursive (respectively recursivelyenumerable). If S is indexed as above...
of the production rules. Such sets are recursivelyenumerablelanguages and every recursivelyenumerablelanguage is the restriction of some such set to...
technological advancement Type-0 language or Recursivelyenumerablelanguage in the Chomsky hierarchy of formal languages Type 0 string theory, a model of...
reducible to non-recursively defined values: in this case F(0) = 0 and F(1) = 1. Applying the standard technique of proof by cases to recursively defined sets...
Kleene's recursion theorem Recursivelyenumerable set Recursivelyenumerablelanguage Decidable language Undecidable language Rice's theorem Post's theorem...
Peano arithmetic) is also recursivelyenumerable, as one can enumerate all the proofs of the theory. While all primitive recursive functions are provably...
if and only if the word w is in the language. The term enumerable has the same etymology as in computably enumerable sets of natural numbers. The following...