Reactive Systems: Modelling, Specification and Verification - Cs.ioc.ee

Chapter 3
Behavioural equivalences
We have previously remarked that CCS, like all other process algebras, can be used
to describe both implementations of processes and specifications of their expected
behaviours. A language like CCS therefore supports the so-called single language
approach to process theory—that is, the approach in which a single language is
used to describe both actual processes and their specifications. An important ingredient
of these languages is therefore a notion of behavioural equivalence or
behavioural approximation between processes. One process description, say SYS,
may describe an implementation, and another, say SPEC, may describe a specification
of the expected behaviour. To say that SYS and SPEC are equivalent is taken
to indicate that these two processes describe essentially the same behaviour, albeit
possibly at different levels of abstraction or refinement. To say that, in some formal
sense, SYS is an approximation of SPEC means roughly that every aspect of the
behaviour of this process is allowed by the specification SPEC, and thus that nothing
unexpected can happen in the behaviour of SYS. This approach to program
verification is also sometimes called implementation verification or equivalence
checking.
3.1 Criteria for a good behavioural equivalence
We have already informally argued that some of the processes that we have met so
far ought to be considered behaviourally equivalent. For instance, we claimed that
the behaviour of the process SmUni defined in equation 2.4 on page 13 should be
considered equivalent to that of the specification
Spec def
= pub.Spec ,
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