Analysis problems for sequential dynamical systems and communicating state machines

Abstract

Informally, a sequential dynamical system (SDS) consists of an undirected graph where each node v is associated with a state sv and a transition function fv. Given the state value sv and thoseo f the neighbors of v, thef unction fv computes the next value of sv. Theno de transition functions are evaluated according to a specified total order. Such a computing device is a mathematical abstraction of a simulation system. We address the complexity of some state reachability problems for SDSs. Our main result is a dichotomy between classes of SDSs for which the statere achability problems arecomp utationally intractablean d thosefor which the problems are efficiently solvable. These results also allow us to obtain stronger lower bounds on the complexity of reachability problems for cellular automata and communicating state machines.