- Published 2008

In the simplest case, the controller synthesis problem asks to find a model for a given specification. So it is just the satisfiability problem. In a more refined version one is given a system, referred to as a plant, and is asked to find a controller such that the controlled system satisfies a given specification. Here, we are interested in the case when both the plant and the controller are distributed systems. More precisely, when they are modelled by asynchronous automata. There are numerous versions of the distributed synthesis problem [PR90, LW90, RW92, KV01, MT01, AVW03, MW03, GLZ04, MTY05]. We focus on two variants that are most rooted in the theory of Mazurkiewicz traces. They correspond to two different, and quite intuitive, ways of controlling a distributed system. The interest in these two control problems is also motivated by the fact that their decidability is still open. This contrasts with most of the other settings where one very quickly hits the undecidability barrier [PR90, MT01, AW07]. In the two problems we consider, the goal is to control the behaviour of an asynchronous automaton. This is an automaton with some fixed number of components, or processes, executing in parallel. Each input letter has a preassigned set of processes it acts on. In this way, if two letters have disjoint sets of assigned processes we can consider that they can occur in parallel. The objective is to control an asynchronous automaton so that every possible run satisfies a given specification. The control consists in forbidding some actions of the automaton, but not every action can be forbidden, and the control has also to ensure that the system does not block completely. In the context of asynchronous automata, it is not reasonable to consider a controller that at every moment of the execution has a complete knowledge of the state of all the processes. This would amount to eliminating all concurrency in the automaton and controlling the resulting finite automaton. Control of finite automata is well studied and much simpler than distributed control [KG95, CL99]. It is much more interesting to try to control an asynchronous automaton without forcing an ad hoc sequentialisation of its behaviours. A

@inproceedings{Muscholl2008ALA,
title={A look at the control of asynchronous automata},
author={Anca Muscholl and Igor Walukiewicz and Marc Zeitoun},
year={2008}
}