The main goal in this paper is to use a dual equivalence in automata theory started in [RBBCL13] and developed in [BBCLR14] to prove a general version of the Eilenberg-type theorem presented in [BBPSE12]. Our principal results confirm the existence of a bijective correspondence between formations of (non-necessarily finite) monoids, that is, classes of monoids closed under taking epimorphic images and finite subdirect products, with formations of languages, which are classes of (non-necessarily regular) formal languages closed under coequational properties. Applications to non-r-disjunctive languages are given.
Additional Metadata
Keywords formations, semigroups, formal languages, automata theory
MSC Solvable groups, theory of formations, Schunck classes, Fitting classes, $\pi$-length, ranks (msc 20D10)
THEME Software (theme 1)
Publisher CWI
Series Formal methods [FM]
Note Published paper: DOI: 10.7561/SACS.2015.2.171
Ballester-Bolinches, A, Cosme-Llopez, E, Esteban-Romero, R, & Rutten, J.J.M.M. (2015). Formations of monoids, congruences, and formal languages . Formal methods [FM]. CWI.