Definitions
There are two equivalent major definitions for the concept of a recursive language:
- A recursive formal language is a recursive subset in the set of all possible words over the alphabet of the language.
- A recursive language is a formal language for which there exists a Turing machine which will, when presented with any finite input string, halt and accept if the string is in the language, and halt and reject otherwise. The Turing machine always halts; it is known as a 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.
Read more about this topic: Recursive Language
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