Seminearring Models of Reversible Computation I Institutsbericht 533

Process Algebra is one of the well{known algebraic models used in theoretical Computer Science, mappings of semigroups are another such model. Both are based upon an algebraic structure known as a seminearring. Reversible Computation is a paradigm of growing importance, adaptions to current tools are of interest in the light of new developments. The extra structure aaorded to the algebraic structure as a result of the imposition of reversible computation requirements leads to a richer and more interesting theory. In this paper I want to report on my earliest investigation of the interplay between these algebraic models of computation and the ideas of reversible computation. I look at various ways in which we could encode the requirements of reversibility of computation into the seminearrings from the Process Algebra and semigroup mappings models of computation. Successive generalisations of the algebraic structure follow, with some surprising results about their equivalences. This paper is a version of Chapter 4 of my Doctoral thesis, "Algebraic Aspects of Reversible Computation". It is primarily a survey paper, containing many questions and observations. Followup papers should begin to answer some of these questions and explain some of the observations.