What is the purpose of the Valiant's algorithm with epsilon transitions in automata theory?

What is the purpose of the Valiant's algorithm with epsilon transitions in automata theory?

The purpose of Valiant's algorithm with epsilon transitions in automata theory is to determine whether a given string can be generated by a given non-deterministic finite automaton (NFA) with epsilon transitions. It is used to solve the membership problem for NFAs with epsilon transitions, which involves determining if a given string belongs to the language defined by the NFA.