Behaviour Algebras

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.