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.
Convergence. Does a system at hand converge on a given initial state configuration?
Path Intersection. Will a system starting in given two state configurations produce a common configuration?
Cycle Length. Since the state space is finite, every BFDS on a given initial state configuration either converges or enters a cycle having length greater than 1. If the latter is the case, what is the length of the loop? Or put more simply, for an integer , is the length of loop greater than ?
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Ogihara, M., & Uchizawa, K. (2015). Computational complexity studies of synchronous boolean finite dynamical systems. In Theory and Applications of Models of Computation – 12th Annual Conference, TAMC 2015, Proceedings (Vol. 9076, pp. 87-98). (Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics); Vol. 9076). Springer Verlag. DOI: 10.1007/978-3-319-17142-5_9