Reversible k-valued logic circuits are finitely generated for odd k
  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. 
Peter Selinger
cs.ET math.RA quant-ph