Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata

Blaise Genest (1) , Hugo Gimbert (2) , Anca Muscholl (2) , Igor Walukiewicz (2)

1 DISTRIBCOM - Distributed and Iterative Algorithms for the Management of Telecommunications Systems
2 LaBRI - Laboratoire Bordelais de Recherche en Informatique

Asynchronous automata are parallel compositions of finite- state processes synchronizing over shared variables. A deep theorem due to Zielonka says that every regular trace language can be represented by a deterministic asynchronous automaton. In this paper we improve the construction, in that the size of the obtained asynchronous automaton is polynomial in the size of a given DFA and simply exponential in the number of processes. We show that our construction is optimal within the class of automata produced by Zielonka-type constructions. In particular, we provide the first non trivial lower bound on the size of asynchronous automata.

Domaines: Logique en informatique [cs.LO]

Blaise Genest, Hugo Gimbert, Anca Muscholl, Igor Walukiewicz. Optimal Zielonka-Type Construction of Deterministic Asynchronous Automata. ICALP, 2010, France. pp.52-63. ⟨hal-00536788⟩