Closures of regular languages for profinite topologies

• Type: Article in International Scientific Journal
• Date: 2014

Authors

Almeida, J (Author) FCUP; Costa, JC (Author) Other; Zeitoun, M (Author) Other

Journal

Title: Semigroup Forum

Vol. 89

Pages: 20-40

ISSN: 0037-1912

Publisher: Springer Nature

Indexing

ISI Web of Knowledge - 3 Citations

Scopus - 4 Citations

Scientific classification

FOS: Natural sciences > Mathematics

Other information

Authenticus ID: P-009-SPN

DOI: 10.1007/s00233-014-9574-3

Abstract (EN): The Pin-Reutenauer algorithm gives a method, that can be viewed as a descriptive procedure, to compute the closure in the free group of a regular language with respect to the Hall topology. A similar descriptive procedure is shown to hold for the pseudovariety of aperiodic semigroups, where the closure is taken in the free aperiodic -semigroup. It is inherited by a subpseudovariety of a given pseudovariety if both of them enjoy the property of being full. The pseudovariety , as well as some of its subpseudovarieties are shown to be full. The interest in such descriptions stems from the fact that, for each of the main pseudovarieties in our examples, the closures of two regular languages are disjoint if and only if the languages can be separated by a language whose syntactic semigroup lies in . In the cases of and of the pseudovariety of semigroups in which all regular elements are idempotents, this is a new result.

Language: English

Type (Professor's evaluation): Scientific