Some Results on Invertible Cellular Automata

A bst ract . V-Ie address certain questions concern ing invert ible cellular aut omata (ICA) , and present new results in this area . Specifically, we explicitly const ru ct a cellular automaton (CA) in a class (r esidual clas s) previously known not to be empty only via a nonconstr uctive existe nce proof. T his class contains CAs that are invert ible on every fini te suppor t but not on an infinite la t t ice. Moreover , we show a class th at contains ICAs having bound ed neighb orh ood , but whose inverses const it ute a class of CAs for which there is no recur sive fun ct ion bo unding all t he neighborhoods.