On recognizable trace languages

Manfred Kufleitner (1) , Pascal Weil (1)

1 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Traces are a classical model of distributed computations. The theory of recognizable trace languages has been developed since the 1980s, but it has failed to achieve the same descriptive power as the theory of languages of finite words. We introduce a new algebraic model to discuss and classify recognizable trace languages, which takes explicitly into account the multiplicative structure, but also the independence structure of the trace monoid. We show that this tool allows the proof of an Eilenberg-like variety theorem, and that it can be used to give an algebraic characterization of the levels of the alternation hierarchy for first-order logic.

Domaines: Logique en informatique [cs.LO]; Mathématique discrète [cs.DM]

Manfred Kufleitner, Pascal Weil. On recognizable trace languages. Conference AutoMathA 2007: Automata from Mathematics to Applications, Jun 2007, Mondello, Italy. ⟨hal-00157974⟩