Affiliations: Institute of Computer Science, Polish Academy of
Sciences, Ordona 21, 01-237 Warszawa, Poland. E-mail: [email protected]
Abstract: The paper is the second part of two-part paper that contributeswith
a concept of a process, with operations allowing to define complex processes in
terms of their components, with the respective algebras, and with the idea of
using the formal tools thus obtained to describe the behaviours of concurrent
systems. In the first part a universal model of a process have been introduced
and operations on processes have been defined. A process is viewed as a model
of a run of a system (discrete, continuous, or of a mixed type). A process may
have an initial state (a source), a final state (a target), or both. A process
can be represented by a partially ordered multiset. Processes of which one is a
continuation of the other can be composed sequentially. Independent processes,
can be composed in parallel. Processes may be prefixes, i.e. independent
components of initial segments of other processes. It has been shown that
processes in a universe of objects and operations on such processes form a
partial algebra, called algebra of processes, that is a specific partial
category with respect to the sequential composition, and a specific partial
monoid with respect to the parallel composition. In the second part the
properties of algebras of processes described in the first part are regarded as
axioms defining a class of abstract partial algebras, called behaviour-oriented
algebras, and properties of such algebras are investigated. In particular, it
is shown how some of the behaviour-oriented algebras can be represented as
algebras of processes, and how to use them to describe phenomena with states
and processes provided with specific structures.
