A Homomorphism Concept for omega-Regularity - Klarlund, Nils (BRICS Report Series, 1994)
The Myhill-Nerode Theorem (that for any regular language, there is a canonical recognizing device) is of paramount importance for the computational handling of many formalisms about finite words. For infinite words, no prior concept of homomorphism or structural comparison seems to have generalized the Myhill-Nerode Theorem in the sense that the concept is both language preserving and representable by automata. In this paper, we propose such a concept based on Families of Right Congruences (Maler and Staiger 93), which we view as a recognizing structures. We also establish an exponential lower and upper bound on the change in size when a representation is reduced to its canonical form.