Logic and bounded-width rational languages of posets over countable scattered linear orderings

International audienc

Logic and bounded-width rational languages of posets over countable scattered linear orderings

International audienc

Logic and branching automata

Abstract. The first result presented in this paper is the closure under complementation of the class of languages of finite N-free posets recognized by branching automata. Relying on this, we propose a logic, named Presburger-MSO or P-MSO for short, precisely as expressive as branching automata. The P-MSO theory of the class of all finite N-free posets is decidable

Automata, semigroups and recognizability of words on ordinals

International audienc

Logic and Branching Automata

In this paper we study the logical aspects of branching automata, as defined by Lodaya and Weil. We first prove that the class of languages of finite N-free posets recognized by branching automata is closed under complementation. Then we define a logic, named P-MSO as it is a extension of monadic second-order logic with Presburger arithmetic, and show that it is precisely as expressive as branching automata. As a consequence of the effectiveness of the construction of one formalism from the other, the P-MSO theory of the class of all finite N-free posets is decidable

Finite automata and ordinals

International audienc

Star-Free Sets of Words on Ordinals

Let n be a fixed integer; we extend the theorem of Schützenberger, McNaughton and Papert on star-free sets of finite words to languages of words of length less than ω^n