Polynomial closure of group languages and open sets of the Hall topology
The aim of this paper is to show that the two classes of recognizable (or regular) languages of the title are actually the same. But a title has to be short and ours does not mention two other important characterizations given in this paper: an algebraic characterization, on which our proofs rely, and a more algorithmic one in terms of finite automata. This gives four possible points of view to look at our class and so, the reader may choose between combinatorics, topology, algebra or automata according to her or his preferences. We present the language perspective, the topological aspects, the algebraic characterization and the connections with automata in this order.
scientific article; zbMATH DE number 983812
scientific article