Behaviour Algebras

Issue title: New Frontiers in Scientific Discovery – Commemorating the Life and Work of Zdzislaw Pawlak

Article type: Research Article

Authors: Winkowski, Józef

Affiliations: Institute of Computer Science, Polish Academy of Sciences, Ordona 21, 01-237 Warszawa, Poland. E-mail: wink@ipipan.waw.pl

Abstract: The paper is concerned with algebras whose elements can be used to represent runs of a system, called processes. These algebras, called behaviour algebras, are categories with respect to a partial binary operation called sequential composition, and they are partial monoids with respect to a partial binary operation called parallel composition. They are characterized by axioms such that their elements and operations can be represented by labelled posets and operations on such posets. The respective representation is obtained without assuming a discrete nature of represented elements. In particular, it remains true for behaviour algebras with infinitely divisible elements, and thus also with elements which can represent continuous and partially continuous processes. An important consequence of the representation of elements of behaviour algebras by labelled posets is that elements of some subalgebras of behaviour algebras can be endowed in a consistent way with structures such as a graph structure etc.

Keywords: Processes, states, sequential composition, parallel composition, category, partial monoid, structure

Journal: Fundamenta Informaticae, vol. 75, no. 1-4, pp. 537-560, 2007