On path equivalence of nondeterministic finite automata

Abstract

Two nondeterministic finite automata (NFAs) are said to be path equivalent if each string is accepted by the two automata via the same number of computation paths. In this paper we show the following. (1) The path equivalence problem for NFAs without lambda-cycles is solvable not only in polynomial sequential time but also in O(log(2)(n)) parallel time using a polynomial number of processors, where n is the total number of states in two NFAs. (2) The path equivalence problem for NFAs with lambda-cycles is PSPACE-complete, hence decidable.