Automata Theory Questions Medium
In the context of Automata Theory, a decidable language refers to a language for which there exists a Turing machine that can determine whether a given input string belongs to the language or not. In other words, there is an algorithmic procedure that can always provide a definite answer (either "yes" or "no") for any input string.
On the other hand, an undecidable language is a language for which there does not exist a Turing machine that can determine whether a given input string belongs to the language or not. In this case, there is no algorithmic procedure that can always provide a definite answer for any input string.
The key difference between decidable and undecidable languages lies in the existence of a Turing machine that can decide the language. If such a Turing machine exists, the language is decidable; otherwise, it is undecidable.
It is worth noting that undecidability does not imply that it is impossible to recognize or generate strings belonging to an undecidable language. It simply means that there is no general algorithm that can decide membership in the language for all possible input strings.