Rational series and their languages
Rational series and their languages
An introduction to symbolic dynamics and coding
An introduction to symbolic dynamics and coding
Enumerative sequences of leaves and nodes in rational trees
Theoretical Computer Science
Automata, Languages, and Machines
Automata, Languages, and Machines
Automata: Theoretic Aspects of Formal Power Series
Automata: Theoretic Aspects of Formal Power Series
A Finite State Version of the Kraft--McMillan Theorem
SIAM Journal on Computing
Bisimulations for fuzzy automata
Fuzzy Sets and Systems
On the equivalence of Z-automata
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Computation of the greatest simulations and bisimulations between fuzzy automata
Fuzzy Sets and Systems
Nondeterministic automata: Equivalence, bisimulations, and uniform relations
Information Sciences: an International Journal
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The main result is a characterization of the generating sequences of the length of words in a regular language on k symbols. We say that a sequence s of integers is regular if there is a finite graph G with two vertices i, t such that sn is the number of paths of length n from i to t in G. Thus the generating sequence of a regular language is regular. We prove that a sequence s is the generating sequence of a regular language on k symbols if and only if both sequences s = (sn)n≥0 and t = (kn − sn)n≥0 are regular.