Automata Theory Questions Medium
In automata theory, a recursive language and a recursively enumerable language are two different types of languages that can be recognized by different types of automata.
A recursive language is a language for which there exists a Turing machine that can decide whether a given input string belongs to the language or not. In other words, a recursive language is a language that can be recognized by a Turing machine that halts on all inputs and gives a definite answer of either "yes" or "no". The Turing machine for a recursive language will always terminate and provide the correct answer.
On the other hand, a recursively enumerable language is a language for which there exists a Turing machine that can recognize whether a given input string belongs to the language or not. However, this Turing machine may not always halt on inputs that do not belong to the language. In other words, a recursively enumerable language is a language that can be recognized by a Turing machine that may either halt and give a definite answer of "yes" for inputs that belong to the language, or it may run indefinitely for inputs that do not belong to the language.
In summary, the main difference between a recursive language and a recursively enumerable language lies in the behavior of the recognizing Turing machine. A recursive language can be recognized by a Turing machine that always halts and provides a definite answer, while a recursively enumerable language can be recognized by a Turing machine that may not always halt on inputs that do not belong to the language.