Analysis Problems for Sequential Dynamical Systems and Communicating State Machines

Christopher L. Barrett, Harry B. Hunt III, Madhav V. Marathe, S. S. Ravi, Daniel J. Rosenkrantz, Richard Edwin Stearns

Abstract: Informally, a sequential dynamical system (SDS) consists of an undirected graph where each node v is associated with a state s v and a transition function f v . Given the state value s v and those of the neighbors of v, the function f v computes the next value of s v . The node 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 state reachability problems are computationally intractable and those for 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.