Generalized reversibility of cellular automata with boundaries

In this paper, cellular automata with boundaries are addressed by using the theories of semi-tensor product and Drazin inverse of matrices. For a cellular automaton with boundaries, a dynamical system model is constructed, then a necessary and sufficient condition for the reversibility is given, and a concept of generalized inverse cellular automaton that characterizes the local energy conservation is presented. Besides, a representation for the (generalized) inverse cellular automaton together with a unified algorithm to calculate it is given. Some examples are given to illustrate the algorithm.