Conclusions
There are two noteworthy aspects of reversibility. One is that there exists a very elaborate and technical theory of injective and surjective mappings which has not dealt extensively with particular examples or applications. On the other hand a variety of empirical methods have been discovered for producing reversible automata, without having had a very extensive theoretical foundation. It would be helpful to reconcile these two tendencies.
The other aspect is the extent to which the theory of reversible automata has been treated in isolation from other cellular automata. This has probably been due to the very special nature of the proofs required, which do not leave much latitude for exceptions or approximations. Nevertheless one doubts that a binary automaton with 1,024 neighborhoods, 511 of which evolve into 0 and 513 of which evolve into 1, is that much different from an automaton whose counterimages balance. In other words, there should be a statistical continuum accounting for nearly reversible rules, almost surjectivity, and the like.
Harold V. McIntosh
E-mail:mcintosh@servidor.unam.mx