Systems, Properties and Refinement within a Process Algebra Framework

Process algebras are mathematical frameworks which can be used to provide behavioural descriptions of systems. The behaviours are described in terms of processes which are autonomous units of behaviour whose evolution are synchronised through the occurrence of events. Within the process algebra there is a class of operators which permit the direct specification of behaviours. The guarding and choice operators allow sequencing of events and branching behaviours. Recursive process definitions permit iterative behaviour to be expressed. Essentially a process description specifies which events can occur in the various states of the process. A second class of operator allows process behaviour to be specified implicitly through derivation from other process behaviours. These operators include composition, abstraction (hiding) and relabelling. The process algebra thus supports the construction of modular descriptions of systems which can be organised in a hierarchical fashion. Recent work [1] has been concerned with expressing and manipulating temporal properties of systems within the process algebra framework. This is in contrast to the approach which has used a modal or temporal logic formalism to express the temporal properties and then employed the technique of model-checking to establish whether the logic formulation of a property is satisfied by a system description. My research has explored the the representation of temporal properties of systems as behaviours within the process algebra framework. There are two distinct aspects to this work. Firstly temporal properties have to be expressed within the process formalism. This can be done by hand, based on a temporal interpretation of the behavioural operators of the process algebra. However for complex properties this technique becomes impractical. An alternative approach of using property patterns was proposed by Dwyer et al [2] based on the design pattern paradigm of Gamma et al [3]. Dwyer et al provided mappings of a selection of property patterns into various formalisms such as temporal logics and regular expressions. My work extended this approach to provide mappings of the property patterns into a process algebra by translation from the regular expression forms. The second aspect of manipulating temporal properties in the process algebra is concerned with testing whether system descriptions satisfy the formulation of the temporal property. Within the process algebra the testing essentially involves a comparison of the process representations of the system and the property concerned. The nature of this comparison is dependent on whether the property represents a safety or a liveness condition. The comparisons can be expressed using a combination of the composition operator and process equivalence. In my work I have defined a comparison between processes which more directly expresses the