Asynchronous Cellular Automata and Asynchronous Automata for Pomsets

Asynchronous cellular automata and asynchronous automata have been introduced by Zielonka [14] for the study of Mazurkiewicz traces. In [2] Droste & Gastin generalized the first to pomsets. We show that the expressiveness of monadic second order logic and asynchronous cellular automata are different in the class of all pomsets without autoconcurrency. Then we introduce a class where the expressivenesses co-incide. This extends the results from [2]. Furthermore, we propose a generalization of trace asynchronous automata for general pomsets. We show that their expressive power coiucides with that of monadic second order logic for a large class of pomsets. The universality and the equivalence of asynchronous automata for pomsets are proved to be decidable which is shown to be false for asynchronous cellular automata.