On the Control of Asynchronous Automata

TL;DR

This paper investigates the decidability of controller synthesis for asynchronous automata, unifying existing results and introducing a new class of plants called decomposable games with decidable synthesis.

Contribution

It introduces decomposable games, a new class of plants with decidable controller synthesis, unifying previous decidability results and expanding the scope of controllable asynchronous automata.

Findings

Decidability of controller synthesis for decomposable games.

Unified proof covering three known decidable classes.

Introduction of new decidable plant examples.

Abstract

The decidability of the distributed version of the Ramadge and Wonham controller synthesis problem,where both the plant and the controllers are modeled as asynchronous automataand the controllers have causal memoryis a challenging open problem.There exist three classes of plants for which the existence of a correct controller with causal memory has been shown decidable: when the dependency graph of actions is series-parallel, when the processes are connectedly communicating and when the dependency graph of processes is a tree. We design a class of plants, called decomposable games, with a decidable controller synthesis problem.This provides a unified proof of the three existing decidability results as well as new examples of decidable plants.