Specification of Reactive Hardware/Software Systems - Electronic ...

9.8 Summary 301
To prepare the development of behaviour-preserving transformation in Chapter 10, we
have made the notion of ’behaviour-preservation’ precise. To this end we have defined
a binary relation, called transformation equivalence, on POOSL specifications.
Transformation equivalence is (indirectly) defined in terms of so-called bisimulations.
Bisimulations, on their turn, are specified in terms of the structural operational semantics
of POOSL. They provide a simple and elegant technique for proving equivalences
between specifications.
Transformation equivalence is strongly related to observation equivalence defined by
Milner for CCS. Observation equivalence has the advantage of being very strong. If two
systems are known to be observation equivalence, then they are also equivalent under
many other equivalence relations. In the context of behaviour-preserving transformations,
this is a very pleasant property.
Although observation equivalence is a very strong relation, it is still too weak to support
behaviour-preserving transformations. The problem is that observation equivalence
only refers to future behaviour of systems. It does therefore not allow transformations
to be carried out correctly during interactive system simulation. Transformation equivalence
remedies this shortcoming by also taking the past behaviour into account. To
demonstrate the applicability of transformation equivalence, we have given a simple
example in which we prove that a simple handshake protocol and a 1-place buffer are
transformation equivalent.
In comparison to semantics found in literature, our semantics may seem rather complex.
In literature, however, semantics are often based on toy languages or on simple and clean
parts of realistic languages. In our case we have given a full semantics of a complex and
realistic language. We think that this justifies the additional complexity.