The set of reversible

The reversibility problem for 90150 cellular automata (both null and periodic boundary) is tackled using continuants and regular expressions. A 90150 cellular automata can be uniquely encoded by a string over the alphabet {0, 1}. It is shown that the set of strings which correspond to reversible 90150 cellular automata is a regular set. We use the regular expression to enumerate the number of reversible strings of a fixed length. As a consequence, it is shown that given a polynomial p(x), it is not always possible to get a 90150 cellular automata whose transition matrix has characteristic polynomial p(x).