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.<br /> <br /> 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.<br /> <br />In this paper, we propose such a concept based on Families

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... f Right Congruences (Maler and Staiger 93), which we view as a recognizing structures.<br /> <br />We also establish an exponential lower and upper bound on the change in size when a representation is reduced to its canonical form.