Affiliations: Institute of Computer Science Polish Academy of
Sciences Ordona 21, 01-237 Warszawa, Poland. E-mail: [email protected]
Abstract: The paper is the first part of a two-part paper that contributes
with a concept of a process viewed as a model of a run of a phenomenon
(discrete, continuous, or of a mixed type), 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. 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 can be a continuation of the
other can be composed sequentially. Independent processes, i.e. processes which
do not disturb each other, can be composed in parallel. Processes may be
prefixes, i.e. independent components of initial segments of other processes. Processes in a universe of objects and operations on such processes form a
partial algebra, called algebra of processes. Algebras of processes are partial
categories with respect to the sequential composition, and partial monoids with
respect to the parallel composition. Algebras of processes can be used to
define behaviours of concurrent systems. The behaviour of a system can be
defined as the set of possible processes of this system with a structure on
this set. Such a set is prefix-closed. The structure on this set reflects the
prefix order and, possibly, specific features of the behaviour like
observability, the relation to flow of real time, etc. Algebras of processes
can also be used to define behaviours, to define operations on behaviours
similar to those in the existing calculi of behaviours, and to define random
behaviours. The first part of the whole paper investigates algebras of
processes and their applications to describing behaviours of systems. 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
behaviouroriented algebras, and they initiate a theory of such algebras.
