Factoriality and the Pin-Reutenauer procedure

• Type: Article in International Scientific Journal
• Date: 2016

Authors

Almeida, J (Author) FCUP; Costa, JoseCarlos (Author) Other; Zeitoun, Marc (Author) Other

Journal

The Journal is awaiting validation by the Administrative Services.

Title: DISCRETE MATHEMATICS AND THEORETICAL COMPUTER SCIENCE

Vol. 18

ISSN: 1462-7264

Indexing

ISI Web of Knowledge - 2 Citations

Scopus - 2 Citations

Other information

Authenticus ID: P-00M-QZG

Abstract (EN): We consider implicit signatures over finite semigroups determined by sets of pseudonatural numbers. We prove that, under relatively simple hypotheses on a pseudovariety V of semigroups, the finitely generated free algebra for the largest such signature is closed under taking factors within the free pro-V semigroup on the same set of generators. Furthermore, we show that the natural analogue of the Pin-Reutenauer descriptive procedure for the closure of a rational language in the free group with respect to the profinite topology holds for the pseudovariety of all finite semigroups. As an application, we establish that a pseudovariety enjoys this property if and only if it is full.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 23