Affiliations: Laboratoire LIAFA, Université de Paris 7, 2, pl. Jussieu, 75251 Paris Cedex 05, France, cc@liafa.jussieu.fr ; http://www.liafa.jussieu.fr/~cc
Note: [] Address for correspondence: Laboratoire LIAFA, Université de Paris 7, 2, pl. Jussieu, 75251 Paris Cedex 05, France
Abstract: The regular languages in the free monoid generated by a finite alphabet A are exactly the languages that are the models of some sentence of the second-order monadic logic of one successor and a unary predicate for each letter. For trace monoids the natural extension obtained by adapting the successor to the partial order underlying the traces is insufficient to capture the family of their rational subsets. We show that these subsets can be expressed by formulas of the form ∃Γφ where φ is a first-order formula over the structure of traces and Γ is an n-ary predicate semantically restricted, where n is the cardinality of the alphabet.
