Polynomial closure of group languages and open sets of the Hall topology

摘要: This main result of this paper states that a recognizable language is open in the Hall topology if and only it belongs to polynomial closure C group languages. A accepted by permutation automaton. The class languages L set are finite unions form L0a1L1 ... anLn, where ai's letters Li's elements L. which sets or infinite We also give combinatorial description these syntactic characterization. Let be A*, let M its monoid P image. Then if, for every s, t idempotent e M, st implies P. Finally, we characterization on minimal automaton leads time algorithm check, given deterministic automaton, whether recognizes C.