Automata Theory Questions Medium
In the context of Automata Theory, the difference between a recursively enumerable language and a recursive language lies in the level of computability or decidability.
A recursively enumerable language, also known as a partially decidable language, refers to a language for which there exists a Turing machine that can accept all the strings in the language, but may either reject or loop indefinitely on strings not in the language. In other words, there is a Turing machine that can generate an output of "yes" for strings in the language, but it may not halt or provide an output for strings not in the language. This means that a recursively enumerable language can be recognized by a Turing machine that halts on all inputs in the language, but may not halt on inputs not in the language.
On the other hand, a recursive language, also known as a decidable language, refers to a language for which there exists a Turing machine that can accept or reject all strings in the language in a finite amount of time. In other words, there is a Turing machine that can always provide an output of either "yes" or "no" for any given input, without entering an infinite loop. This means that a recursive language can be recognized by a Turing machine that halts on all inputs, providing a definitive answer of acceptance or rejection.
In summary, the main difference between a recursively enumerable language and a recursive language is that a recursively enumerable language can be recognized by a Turing machine that halts on all inputs in the language, but may not halt on inputs not in the language, while a recursive language can be recognized by a Turing machine that always halts and provides a definitive answer for any given input.