Decidable language
A
decidable or
recursive language is a
formal language that is a
recursive set, i.e., for which there exists an
algorithm to solve the following
decision problem: Given
string w, does
w belong to the language? The algorithm is not allowed to run into an infinite loop and has to produce a YES/NO answer for any input string after a finite amount of time. To formalize the rather vague term "algorithm", one usually employs
Turing machines, but several other equivalent approaches are possible.
All regular, context-free and context-sensitive languages are recursive, but there exist recursively enumerable languagess that are not recursive; one example is given by the halting problem.