Distributed Asynchronous Games With Causal Memory are Undecidable

TL;DR

This paper proves that determining the existence of a distributed control strategy in asynchronous automata with causal memory is fundamentally undecidable, highlighting intrinsic limitations in such distributed systems.

Contribution

It establishes the undecidability of the distributed control problem under causal memory, extending understanding of limitations in asynchronous automaton control.

Findings

Undecidability of the control problem for asynchronous automata with causal memory

Controllers cannot always determine a winning strategy in such systems

Highlights fundamental computational limits in distributed control scenarios

Abstract

We show the undecidability of the distributed control problem when the plant is an asynchronous automaton, the controllers use causal memory and the goal of the controllers is to put each process in a local accepting state.