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

10.8 Summary 331
are transformation equivalent and that only differ with respect to their boundaries
and channels, but for which the one specification cannot be transformed into the other
one. This incompleteness result is fundamental. It cannot be solved by adding more
transformations to the transformation system. Of course, this is a theoretical result. In
a practical sense we feel that we have created a transformation system that is able to
transform many complex real-life systems.
Next to the incompleteness result described above, another incompleteness result has
been proven. For each specification there exists an infinite number of other specifications
that are transformation equivalent, but for which no sequences of transformations
exist that transform the former specification into the latter ones. This incompleteness
result leads us to a fundamental limitation of transformational design. The choice of
an initial specification model determines whether or not a satisfying implementation
model is derivable using transformational design. Therefore it is important to consider
implementation-oriented aspects during specification. This statement confirms one of
the basic ideas of this whole thesis.
The research into behaviour-preserving transformations does not finish with this chapter.
For a description of future research topics concerning behaviour-preserving transformations
we refer to Chapter 13.