Recursive language: Difference between revisions

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# A recursive formal language is a [[recursive set|recursive]] [[subset]] in the [[set (mathematics)|set]] of all possible words over the [[alphabet]] of the [[formal language|language]].
# A recursive language is a formal language for which there exists a [[Turing machine]] that, when presented with any finite input [[literal string|string]], halts and acceptaccepts if the string is in the language, and halts and rejects otherwise. The Turing machine always halts: it is known as a [[Machine that always halts|decider]] and is said to ''decide'' the recursive language.
 
By the second definition, any [[decision problem]] can be shown to be decidable by exhibiting an [[algorithm]] for it that terminates on all inputs. An [[undecidable problem]] is a problem that is not decidable.