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Recursively enumerable language information


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.

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Recursively enumerable language

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enumerable languages is called RE. There are three equivalent definitions of a recursively enumerable language: A recursively enumerable language is a recursively...

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Computably enumerable set

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theory, a set S of natural numbers is called computably enumerable (c.e.), recursively enumerable (r.e.), semidecidable, partially decidable, listable,...

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Recursive language

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This type of language was not defined in the Chomsky hierarchy of (Chomsky 1959). All recursive languages are also recursively enumerable. All regular...

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Computability

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recursively enumerable, but not recursive? And, furthermore, are there languages which are not even recursively enumerable? The halting problem is one of...

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Unrestricted grammar

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Recursively enumerable languages are closed under Kleene star, concatenation, union, and intersection, but not under set difference; see Recursively enumerable...

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Computable set

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nondecreasing total computable function is computable. Recursively enumerable language Recursive language Recursion Cutland, N. Computability. Cambridge University...

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Chomsky hierarchy

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context-free language is context-sensitive, every context-sensitive language is recursive and every recursive language is recursively enumerable. These are...

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Abstract family of languages

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context-free languages and the recursively enumerable languages, and other families of formal languages studied in the scientific literature. A formal language is...

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Quotient of a formal language

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context free languages can be any recursively enumerable language. The quotient of two recursively enumerable languages is recursively enumerable. These closure...

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Turing degree

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the language ⟨ ≤, = ⟩. A degree is called recursively enumerable (r.e.) or computably enumerable (c.e.) if it contains a recursively enumerable set....

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Enumeration

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computable. The set being enumerated is then called recursively enumerable (or computably enumerable in more contemporary language), referring to the use...

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Turing recognizable

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%5B%5BWikipedia%3ARedirects+for+discussion%5D%5D+debate+closed+as+delete #REDIRECT Recursively enumerable language...

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List of formal language and literal string topics

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grammar Prefix grammar Pumping lemma Recursively enumerable language Regular expression Regular grammar Regular language S-attributed grammar Star height...

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JFLAP

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automaton pumping lemma for context-free language CYK parser LL parser SLR parser Topics on recursively enumerable language: Turing machine unrestricted grammar...

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Turing machine

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alphabet. A set of strings which can be enumerated in this manner is called a recursively enumerable language. The Turing machine can equivalently be...

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Universal Turing machine

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machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable language. According to the Church–Turing...

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Presentation of a group

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call a subset U of FS recursive (respectively recursively enumerable) if f(U) is recursive (respectively recursively enumerable). If S is indexed as above...

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Post canonical system

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of the production rules. Such sets are recursively enumerable languages and every recursively enumerable language is the restriction of some such set to...

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Type 0

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technological advancement Type-0 language or Recursively enumerable language in the Chomsky hierarchy of formal languages Type 0 string theory, a model of...

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Recursion

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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...

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List of mathematical logic topics

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Kleene's recursion theorem Recursively enumerable set Recursively enumerable language Decidable language Undecidable language Rice's theorem Post's theorem...

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Primitive recursive function

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Peano arithmetic) is also recursively enumerable, as one can enumerate all the proofs of the theory. While all primitive recursive functions are provably...

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Computable function

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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...

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