5 research outputs found

    The Degree of a Finite Set of Words

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    We generalize the notions of the degree and composition from uniquely decipherable codes to arbitrary finite sets of words. We prove that if X = Y?Z is a composition of finite sets of words with Y complete, then d(X) = d(Y) ? d(Z), where d(T) is the degree of T. We also show that a finite set is synchronizing if and only if its degree equals one. This is done by considering, for an arbitrary finite set X of words, the transition monoid of an automaton recognizing X^* with multiplicities. We prove a number of results for such monoids, which generalize corresponding results for unambiguous monoids of relations

    Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics

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    Proceedings of the Fourth Russian Finnish Symposium on Discrete Mathematics

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    A Magyar Tudományos Akadémia Matematikai Kutató Intézetének közleményei

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