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  2. Recursively enumerable language - Wikipedia

    en.wikipedia.org/.../Recursively_enumerable_language

    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.

  3. RE (complexity) - Wikipedia

    en.wikipedia.org/wiki/RE_(complexity)

    The set of recursive languages is a subset of both RE and co-RE. [3] In fact, it is the intersection of those two classes, because we can decide any problem for which there exists a recogniser and also a co-recogniser by simply interleaving them until one obtains a result.

  4. Computably enumerable set - Wikipedia

    en.wikipedia.org/wiki/Computably_enumerable_set

    The definition of a computably enumerable set as the domain of a partial function, rather than the range of a total computable function, is common in contemporary texts. This choice is motivated by the fact that in generalized recursion theories, such as α-recursion theory, the definition corresponding to domains has been found to be more ...

  5. Recursive language - Wikipedia

    en.wikipedia.org/wiki/Recursive_language

    A recursive language is a formal language for which there exists a Turing machine that, when presented with any finite input string, halts and accepts if the string is in the language, and halts and rejects otherwise. The Turing machine always halts: it is known as a decider and is said to decide the recursive language. By the second definition ...

  6. Computable set - Wikipedia

    en.wikipedia.org/wiki/Computable_set

    A more general class of sets than the computable ones consists of the computably enumerable (c.e.) sets, also called semidecidable sets. For these sets, it is only required that there is an algorithm that correctly decides when a number is in the set; the algorithm may give no answer (but not the wrong answer) for numbers not in the set.

  7. Universal Turing machine - Wikipedia

    en.wikipedia.org/wiki/Universal_Turing_machine

    A universal Turing machine can calculate any recursive function, decide any recursive language, and accept any recursively enumerable language. According to the Church–Turing thesis , the problems solvable by a universal Turing machine are exactly those problems solvable by an algorithm or an effective method of computation , for any ...

  8. Unrestricted grammar - Wikipedia

    en.wikipedia.org/wiki/Unrestricted_grammar

    Recursively enumerable languages are closed under Kleene star, concatenation, union, and intersection, but not under set difference; see Recursively enumerable language#Closure properties. The equivalence of unrestricted grammars to Turing machines implies the existence of a universal unrestricted grammar, a grammar capable of accepting any ...

  9. Computable function - Wikipedia

    en.wikipedia.org/wiki/Computable_function

    A language is called computable (synonyms: recursive, decidable) if there is a computable function f such that for each word w over the alphabet, f(w) = 1 if the word is in the language and f(w) = 0 if the word is not in the language. Thus a language is computable just in case there is a procedure that is able to correctly tell whether ...