Formations of Monoids, Congruences, and Formal Languages

Scientific Annals of Computer Science

article

A. Ballester-Bolinches¹  E. Cosme-Llópez¹  R. Esteban-Romero¹  J.J.M.M. Rutten³ 

[1] Departament d’Algebra, Universitat de Val`encia;Institut Universitari de Matem`atica Pura I Aplicada, Universitat Polit`ecnica de Val`encia, Cam´I de Vera;Centrum Wiskunde & Informatica;Radboud Universiteit Nijmegen

关键词: formations;    semigroups;    formal languages;    automata theory;   

DOI  :  10.7561/SACS.2015.2.171

来源: Alexandru Ioan Cuza University of Iasi

【 摘 要 】

The main goal in this paper is to use a dual equivalence in automata theory started in [25] and developed in [3] to prove a general version of the Eilenberg-type theorem presented in [4]. Our principal results confirm the existence of a bijective correspondence between three concepts; formations of monoids, formations of languages and formations of congruences. The result does not require finiteness on monoids, nor regularity on languages nor finite index conditions on congruences. We relate our work to other results in the field and we include applications to non-r-disjunctive languages, Reiterman’s equational description of pseudovarieties and varieties of monoids.

【 授权许可】

CC BY-ND