Which class of languages has a Turing machine that can enumerate all valid strings of the language, but may not halt for invalid strings?

• A. Recursively Enumerable Languages
• B. Regular Languages
• C. Context-Free Languages
• D. Decidable Languages

Answer: (A)

Recursively Enumerable Languages are the ones where a Turing machine can generate or recognize all strings that belong to the language, but it need not halt on strings not in the language. This means membership is semi-decidable: if a string is in the language, the machine will eventually handle it (for example, output it or accept it); if the string is not in the language, the machine may run forever instead of giving a definite reject.

This matches the idea of enumerating all valid strings: you can list every string that should be in the language, but you’re not guaranteed to halt for strings outside it. In contrast, regular and context-free languages have machines (finite automata or pushdown automata) that always decide membership by halting with yes or no, and decidable languages require halting on all inputs. So the class described is Recursively Enumerable Languages.