Analysis Problems for Sequential Dynamical Systems and Communicating State Machines

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 those of the neighbors of v, the function 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 state reachability problems arecomp utationally intractablean d 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.

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