Computational complexity studies of synchronous Boolean finite dynamical systems on directed graphs

A finite dynamical system is a system consisting of some finite number of objects that take upon a value from some domain as a state, in which after initialization the states of the objects are updated based upon the states of the other objects and themselves according to a certain update schedule. This paper studies a subclass of finite dynamical systems the synchronous Boolean finite dynamical system (synchronous BFDS, for short), where the states are Boolean and the state update takes place in discrete time and at the same on all objects. The paper is concerned with three problems, Convergence, Path Intersection, and Cycle Length, of the synchronous BFDS in which the state update functions (or the local state transition functions) are chosen from a predetermined finite basis of Boolean functions B. The paper results characterize their computational complexity.