Languages associated with saturated formations of groups

Languages associated with saturated formations of groups

In a previous paper, the authors have shown that Eilenberg’s variety theorem can be extended to more general structures, called formations. In this paper, we give a general method to describe the languages corresponding to saturated formations of groups, which are widely studied in group theory. We recover in this way a number of known results about the languages corresponding to the classes of...

Transversely Isotropic Saturated Porous Formations

The wavefields generated by monopole and dipole sources in a fluid filled borehole embedded in multilayered transversely isotropic saturated porous formations are studied. The layers are modeled following Biot theory modified in accordance with homogenization theory. It allows to take into account a transversely isotropic skeleton and/or a transversely isotropic complex permeability tensor. The...

Formations of Monoids, Congruences, and Formal Languages

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 ima...

Recognizable Transductions, Saturated Transducers and Edit Languages

Recognizable transductions constitute a well known, proper subclass of rational transductions. To our knowledge, there has been no characterization of recognizable transductions by a well-defined subclass of transducers. In this work we observe that there is a connection between recognizable transductions and languages consisting of edit strings. More specifically, we define a saturated transdu...

Errata to "Formations of Monoids, Congruences, and Formal Languages"