Integrating the Z notation and behavioural formalisms

Abstract: The last several years have witnessed an increasing interest in integrating different formalisms in the formal methods research community. Particularly a number of notations have been proposed by different authors which integrate existing state-based formalisms such as Z, VDM and B and behavioural formalisms such as CCS, CSP and Statecharts. Those state-based formalisms are widely used both in academia and industry, but lack capabilities to capture the concurrency aspect of computer systems. On the other hand, behavioural formalisms have opposite properties, thereby it is expected that integration of both formalisms would compensate their respective shortcomings. The integration of different formalisms was motivated by the need to integrate multiple aspects of computer systems by using corresponding formalisms. That research has raised several interesting research issues such as integration of two underlying semantics and refinement of integrated formalisms. In this thesis, we focus on integration of the Z notation and behavioural formalisms and report two integrations, i.e., Z and first-order logics in terms of labeled transition systems, and Z and a process algebra CCS. The former integration is aimed at providing a formal language for declaring properties in Z and the latter is to give behavioural meanings to Z specifications. Those two integrations are achieved by adopting the same semantic method in which a Z specification is embedded in a labeled transition system. Labeled transition systems are the most widely used operational (behavioural) semantic frameworks which enable us to declare constraints and properties of Z by predicate logics in terms of labeled transition systems as well as semantic integration of Z and the value-passing CCS.