Equivalence Problems for Mappings on Infinite Strings

This paper is concerned with sets of infinite strings (ω-languages) and mappings between them. The main result is that there is an algorithm for testing the (string by string) equality of two homomorphisms on an ω-regular set of infinite strings. As a corollary we show that it is decidable whether two functional finite-state transducers define the same function on infinite strings (are ω-equivalent).