A polynomial time algorithm for the equivalence of two morphisms on ω-regular languages

Abstract

Let L \(\subseteq\) Aω be an ω-regular language given by means of a non-deterministic Buchi automaton M. Let f,g: A∞ → B∞ be two morphisms. We give an algorithm to decide whether f and g are equivalent (word by word) on L. This algorithm has time complexity 0(mn3), where n is the number of arcs of M and m is the size of f and g. This result improves the only known algorithm for this problem which is exponential time [3].