Adding modular predicates

Luc Dartois (1) , Charles Paperman (2)

1 Automate
2 LIAFA - Laboratoire d'informatique Algorithmique : Fondements et Applications

This paper is a contribution to the study of regular languages defined by fragments of first order or even monadic second order logic. More specifically, we consider the operation of enriching a given fragment by adding modular predicates. Our first result gives a simple algebraic counterpart to this operation in terms of semidirect products of varieties together with a combinatorial description based on elementary operations on languages. Now, a difficult question is to know whether the decidability of a given fragment is preserved under this enrichment. We first prove that this is always the case for so-called local varieties. The problem is then reduced to the decidability of varieties of categories. Our main results gives several sufficient conditions to preserve decidability. We use these latter results to establish the decidability of three fragments of the first order logic with two variables.

Mots clés: logic; regular languages; modular predicates; wreath product; varieties; categories

Domaines: Logique en informatique [cs.LO]; Théorie et langage formel [cs.FL]

Luc Dartois, Charles Paperman. Adding modular predicates. 2014. ⟨hal-00934622v2⟩