Additive Automata On Graphs

A bstract. We study cellular automata. with addi tive rules on finite undi rect ed graphs. The addition is carried ou t in some finit e abelian monoid. We investigate the prob lem of deciding wheth er a given con­ figuration has a predecessor . Depending on th e underl ying monoid this prob lem is solvable in polynomial t ime or NP-complete. Fur­ t hermo re, we st udy t he global reversibility of cellular graph automata based on addition modulo two . We give a linear t ime algorithm to decide reversibility of unicyclic graphs. 1. I ntroduction