Group structured linear cellular automata over Zm

摘要

In this paper, we introduce group structured linear cellular automata which appear naturally in the process of finding their inverse automata and show that the set of local maps of such automata forms a group with the star operation and the problem of finding its inverse linear cellular automaton can be reduced to that of finding its inverse element of the group. Furthermore, it is shown that such groups regardless of their scopes are isomorphic to each other.