In this talk I will outline an adaption of the long standing theory of
clones to deal with reversible computation. Reversible computation has
been investigated intensely for several reasons for several decades, the
fundamental work of Toffoli and others laying some basis upon which
developments such as quantum computation is building. The theory of
clones is a way of thinking about the computation possible with certain
functions. Most importantly, clone theory has found a way of describing
closed sets of functions equivalently by their generators or by the
relational structures they preserve, the dual structure of clones.
I will introduce the algebraic techniques used and show how we can
replicate and generalise the results from Toffoli's 1980 paper on
reversible computation. Looking beyond binary state sets, we find that
some restrictions that he found do not apply. We will then look at some
of the possible generalisations of the relations, at possible dual
structures for reversible clone theory.