Asynchronous cellular automata for pomsets without auto-concurrency

Abstract

This paper extends to pomsets without auto-concurrency the fundamental notion of asynchronous cellular automata (AGA) which was originally introduced for traces by Zielonka. We generalize to pomsets the notion of asynchronous mapping introduced by Zielonka and we show how to construct a deterministic ACA from an asynchronous mapping. Our main result generalizes Büchi’s theorem for a class of pomsets without auto-concurrency which satisfy a natural axiom. This axiom ensures that an asynchronous cellular automaton works on the pomset as a concurrent read owner write machine. More precisely, we prove the equivalence between non deterministic AGA, deterministic ACA and monadic second order logic for this class of pomsets.