Formal Languages Questions Medium
In the context of formal languages, a recursively enumerable language and a recursively enumerable set refer to two related but distinct concepts.
A recursively enumerable language is a language that can be recognized by a Turing machine. In other words, there exists a Turing machine that, given any input string belonging to the language, will eventually halt and accept the string as a valid member of the language. However, if the input string does not belong to the language, the Turing machine may either halt and reject the string or run indefinitely without halting.
On the other hand, a recursively enumerable set refers to a set of natural numbers that can be enumerated by a Turing machine. An enumeration of a set means that the Turing machine can generate a sequence of natural numbers, where every member of the set will eventually appear in the sequence. However, the Turing machine may also generate additional numbers that do not belong to the set.
In summary, the main difference between a recursively enumerable language and a recursively enumerable set lies in their respective domains. A recursively enumerable language deals with strings and their recognition, while a recursively enumerable set deals with natural numbers and their enumeration.