A topological approach to transductions

• Type: Article in International Scientific Journal
• Date: 2005

Authors

Jean-Eric Pin (Author) Other; Pedro V. Silva (Author) FCUP

Journal

Title: Theoretical Computer Science

Vol. 340

Pages: 443-456

ISSN: 0304-3975

Publisher: Elsevier

Indexing

ISI Web of Knowledge - 9 Citations

ISI Web of Science

Scopus - 13 Citations

Scientific classification

FOS: Natural sciences

Other information

Authenticus ID: P-000-2T2

DOI: 10.1016/j.tcs.2005.03.029

Abstract (EN): This paper is a contribution to the mathematical foundations of the theory of automata. We give a topological characterization of the transductions tau from a monoid M into a monoid N, such that if R is a recognizable subset of N, tau(-1) (R) is a recognizable subset of M. We impose two conditions on the monoids, which are fullfilled in all cases of practical interest: the monoids must be residually finite and, for every positive integer n, must have only finitely many congruences of index n. Our solution proceeds in two steps. First we show that such a monoid, equipped with the so-called Hall distance, is a metric space whose completion is compact. Next we prove that tau can be lifted to a map tau from M into the set of compact subsets of the completion of N. This latter set, equipped with the Hausdorff metric, is again a compact monoid. Finally, our main result states that tau(-1) preserves recognizable sets if and only if is continuous.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 14