recursively enumerable languages

Recursively enumerable languages are sets of strings for which there exists a computer program that can list all the strings in the set, possibly without end. If a string belongs to the set, the program will eventually find and display it; if not, the program may run forever without giving a definitive answer. This concept captures languages that are "semi-decidable," where membership can be confirmed but not always conclusively negated. It’s a foundational idea in automata theory and computability, describing the limits of what machines can recognize or generate through systematic enumeration.