Reversibility of d-State Finite Cellular Automata

This paper investigates reversibility properties of 1-dimensional 3-neighborhood d-state finite cellular automata (CAs) under periodic boundary condition. A tool named reachability tree has been developed from de Bruijn graph which represents all possible reachable configurations of an n-cell CA. This tool has been used to test reversibility of CAs. We have identified a large set of reversible CAs using this tool by following some greedy strategies. Our conjecture is that the reversible CAs, defined over infinite lattice, are always reversible when the CAs are finite. However, the reverse may not be true.