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.