The Degree of a Finite Set of Words - Models and Algorithms
Communication Dans Un Congrès Année : 2020

The Degree of a Finite Set of Words

Résumé

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.
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hal-04491375 , version 1 (06-03-2024)

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Dominique Perrin, Andrew Ryzhikov. The Degree of a Finite Set of Words. FSTTCS 2020, Dec 2020, Goa (online), India. pp.54:1-54:16, ⟨10.4230/LIPICS.FSTTCS.2020.54⟩. ⟨hal-04491375⟩
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