Synchronization and simplification

On some properties of the syntactic semigroup of a very pure subsemigroup

“…This last resuit and another equivalent proposition concerning the structure of the 0-minimal idéal of the syntactic semigroups S (A), give a characterization of free subsemigroups, of a free semigroup, having a bounded synchronization delay which is more gênerai than that of the theorem of Restivo [11], and also that of a recent resuit obtained by the author, D. Perrin, A. Restivo and S. Termini [3] under the hypothesis that A is finitely gênerated.…”

“…The équivalence of P x and P 2 has been proved by Hashiguchi and Honda [6]. An algebraic proof of the équivalence of P x , P 4 , P 5 and P 6 is in De Luca, Perrin, Restivo and Termini [3].…”

Representation of (Left) Ideal Regular Languages by Synchronizing Automata

“…Hence it is quite natural to ask in which cases the minimal automaton recognizing a given regular language L is synchronized by some word from L. Here we answer this question by proving a criterion for the minimal automaton recognizing L to be synchronized by some word from L. We state this criterion in terms of the notion of a constant of L introduced by Schützenberger [18]. The notion of a constant is widely studied and finds applications in bioinformatics and coding theory [2,8].…”