Reversible k-valued logic circuits are finitely generated for odd k

TL;DR

This paper confirms that reversible k-valued logic circuits are finitely generated when k is odd, providing the proof originally cited privately by Lafont, thus clarifying an important aspect of algebraic circuit theory.

Contribution

It makes publicly available the proof that reversible k-valued logic circuits are finitely generated for odd k, previously only cited privately by Lafont.

Findings

Reversible k-valued logic circuits are finitely generated for odd k

Provides the proof originally cited privately by Lafont

Clarifies algebraic properties of reversible circuits

Abstract

In his 2003 paper "Towards an algebraic theory of Boolean circuits", Lafont notes that the class of reversible circuits over a set of k truth values is finitely generated when k is odd. He cites a private communication for the proof. The purpose of this short note is to make the content of that communication available.