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

10.7 On the Fundamental Limitations of Transformational Design 329
is fundamental. Whatever transformation system is used, it will always partition the
design (model) space into an number of disjoint sub-spaces, each of which is closed
under transformation 13 . Figure 10.5 visualises three different sub-spaces. It is however
not hard to prove that in reality there exist an infinite number of them! This is visualised
in Figure 10.6.
An 'Arbitrary'
Initial
Specification
Model
Figure 10.6: An Infinite Partitioning of the Design Space
This leads us to a fundamental limitation of transformational design. Starting from an
initial model, one is only able to investigate a very limited part of the complete design
space. The part that can actually be investigated depends on the choice of the initial
specification model. Hence:
The choice of an initial specification model determines whether or
not a satisfying implementation model is derivable using transformational
design!
To be able to find an ’optimal’ implementation model it is thus of utter importance
to construct the initial specification model in a very careful way. For if an ’arbitrary’
initial specification is constructed, it is well imaginable that an ’optimal’ implementation
13 This means that it is impossible to transform a model of one sub-space into a model that lies in another
sub-space.