Edited sentence: , it is decidable, but it is not likely that there is an efficient (centralised, parallel or distributed) algorithm that solves the problem in the case of large networks.A complementary research problem is studying the properties of a given distributed system.However, there are many interesting special cases that are decidable.In particular, it is possible to reason about the behaviour of a network of finite-state machines.One example is telling whether a given network of interacting (asynchronous and non-deterministic) finite-state machines can reach a deadlock.So far the focus has been on designing a distributed system that solves a given problem.The halting problem is an analogous example from the field of centralised computation: we are given a computer program and the task is to decide whether it halts or runs forever.The halting problem is undecidable in the general case, and naturally understanding the behaviour of a computer network is at least as hard as understanding the behaviour of one computer.This problem is PSPACE-complete, i