On Some Dynamical Properties of Finite Cellular Automaton

Some characteristics of the global function of the finite cellular automaton (FCA) are investigated. First, a necessary and sufficient condition for a function from the configuration set to itself to be realized by means of an FCA is given. Next, using these results, the realizability of cycle and tree type transition structures is discussed. Especially, for the system of binary 3-neighbor FCA, the realizability of the maximal cycle length and the bijectivity of the global function are investigated. For the system of FCA, each passive configuration set is defined. An algorithm to obtain the spectrum of a passive configuration set is also discussed. In addition, some examples on the spectrum for the system of binary 3-neighbor FCA are demonstrated.