Injectivity and surjectivity of parallel maps for cellular automata

摘要

We define four new properties of parallel maps for cellular automata, viz., strong surjectiveness, weak surjectiveness, strong injectiveness, and weak injectiveness. Of these, the first two are nonequivalent to previously known properties, and bridge the gap between bijectiveness and surjectiveness. On the other hand, the other two properties are proved to be equivalent to surjectiveness. Furthermore, these notions are characterized by strengthened balanced conditions.