Firing Squad Synchronization Problem in Reversible Cellular Automata

We studied the Firing Squad Synchronization Problem (FSSP) on reversible (i.e., backward deterministic) cellular automata (RCA). First we proved that, in the case of RCA, there is no solution under the usual condition for FSSP where the firing state is only one. So we defined a little weaker condition suitable for RCA in which finite number of firing states are allowed. We showed that Minsky’s solution in time 3n can be embedded in an RCA with 99 states that satisfies the new condition. We used the framework of partitioned CA (PCA), which is regarded as a subclass of CA, for making ease of constructing RCA. 1 Dept. of Industrial and Systems Engineering, Faculty of Engineering, Hiroshima University, HigashiHiroshima-shi, 739, Japan, Fax.: +81-824-22-7195, E-mail: [email protected]