Inferring local transition functions of discrete dynamical systems from observations of system behavior

We consider the problem of inferring the local transition functions of discrete dynamical systems from observed behavior. Our focus is on synchronous systems whose local transition functions are threshold functions. We assume that the topology of the system is known and that the goal is to infer a threshold value for each node so that the system produces the observed behavior. We show that some of these inference problems are efficiently solvable while others are NP-complete, even when the underlying graph of the dynamical system is a simple path. We identify a fixed parameter tractable problem in this context. We also consider constrained versions of threshold inference problems where the input includes a set of equality or inequality constraints (which specify pairs of nodes which must have the same threshold value or different threshold values). We present algorithmic and complexity results for several constrained threshold inference problems.