What is the difference between a decidable and undecidable language?

Automata Theory Questions



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What is the difference between a decidable and undecidable language?

In 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 algorithm that can always provide a correct answer within a finite amount of time.

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 other words, there is no algorithm that can always provide a correct answer within a finite amount of time.

In summary, the main difference between a decidable and undecidable language lies in the existence of an algorithm that can determine membership in the language.