Some Results on Reversible Gate Classes Over Non-Binary Alphabets

We present a collection of results concerning the structure of reversible gate classes over non-binary alphabets, including (1) a reversible gate class over non-binary alphabets that is not finitely generated (2) an explicit set of generators for the class of all gates, the class of all conservative gates, and a class of generalizations of the two (3) an embedding of the poset of reversible gate classes over an alphabet of size k into that of an alphabet of size k + 1 (4) a classification of gate classes containing the class of (k − 1, 1)-conservative gates, meaning gates that preserve the number of occurrences of a certain element in the alphabet.