Hybrid one-dimensional reversible cellular automata are regular

It is shown that the set of hybrid one-dimensional reversible cellular automata (CA) with the periodic boundary condition is a regular set. This has several important consequences. For example, it allows checking whether a given CA is reversible and the random generation of a reversible CA from the uniform distribution, both using time polynomial in the size of the CA. Unfortunately, the constant term in the resulting random generation algorithm is much too large to be of practical use. We show that for the less general case of null boundary (NB) CA, this constant can be reduced drastically, hence facilitating a practical algorithm for uniform random generation. Our techniques are further applied asymptotically to count the number of reversible NBCA.