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Journals and Conferences
Černý’s conjecture asserts the existence of a synchronizing word of length at most (n− 1) for any synchronized n-state deterministic automaton. We prove a quadratic upper bound on the length of a synchronizing word for any synchronized n-state deterministic automaton satisfying the following additional property: there is a letter a such that for any pair of… (More)
We prove that two automata with multiplicity in Z are equivalent, i.e. define the same rational series, if and only if there is a sequence of Z-coverings, co-Z-coverings, and circulations of −1, which transforms one automaton into the other. Moreover, the construction of these transformations is effective. This is obtained by combining two results: the… (More)
We described here a construction on transducers that give a new conceptual proof for two classical decidability results on transducers: it is decidable whether a nite transducer realizes a functional relation, and whether a nite transducer realizes a sequential relation. A better complexity follows then for the two decision procedures.
We show that two equivalent K-automata are conjugate to a third one, when K is equal to B, N, Z, or any (skew) field and that the same holds true for functional tranducers as well.
We study the class of periodic-finite-type (PFT) shift spaces, which can be used to model time-varying constrained codes used in digital magnetic recording systems. A PFT shift is determined by a finite list of periodically forbidden words. We show that the class of PFT shifts properly contains all finite-type (FT) shifts, and the class of almost… (More)
We study whether the entropy (or growth rate) of minimal forbidden patterns of symbolic dynamical shifts of dimension 2 or more, is a conjugacy invariant. We prove that the entropy of minimal forbidden patterns is a conjugacy invariant for uniformly semi-strongly irreducible shifts. We prove a weaker invariant in the general case.
We give a quadratic-time algorithm to compute the set of minimal forbidden words of a factorial regular language. We give a linear-time algorithm to compute the minimal forbidden words of a finite set of words. This extends a previous result given for the case of a single word only. We also give quadratic-time algorithms to check whether a regular language… (More)
The main result is a characterization of the generating sequences of the length of words in a regular language on <i>k</i> symbols. We say that a sequence <i>s</i> of integers is regular if there is a finite graph <i>G</i> with two vertices <i>i, t</i> such that <i>s</i><sub><i>n</i></sub> is the number of paths of length <i>n</i> from <i>i</i> to <i>t</i>… (More)
We develop a O(m log n)-time and O(k + n + m)-space algorithm for minimizing incomplete deterministic automata, where n is the number of states, m the number of edges, and k the size of the alphabet. Minimization reduces to the partial Functional coarsest partition problem. Our algorithm is a slight variant of Hopcroft’s algorithm for minimizing… (More)