A quadratic construction for Zielonka automata with acyclic communication structure

Abstract

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 recognized by a deterministic asynchronous automaton. The construction is rather involved and the most efficient variant produces automata which are exponential in the number of processes and polynomial in the size of the DFA.In this paper we show a simple, quadratic construction in the case where the synchronization actions are binary and define an acyclic communication graph.