A formal language is decidable if a Turing machine halts on every input and correctly determines membership. Equivalently its encoded words form a recursive set. A computably enumerable language requires only a machine that eventually accepts every member; it may run forever on nonmembers.
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A recursive language (also known as a decidable language) is a type of formal language in the field of computer science and computational theory. Specifically, a recursive language is a set of strings over a given alphabet for which there exists a Turing machine that will accept every string in the language and will reject (or halt) every string that is not in the language.
