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

308 Behaviour-Preserving Transformations
(7) If a channel is internally (at the side of the inner name) connected to another
channel, the outer name of the latter channel may be deleted.
(8) If an arc only connects channels at the side of their outer names, then these outer
names may be deleted and joined into a single name given to the arc itself.
The following picture represents ISD(C c § E1 ¥ E2 ¥ Sys p ) of rule (2), after application of rules
(6), (7) and (8).
c d
C(E ,...,E )
a b
The 8 rules given in this section should be interpreted as a basic framework for drawing
Instance Structure Diagrams. In the case of complex diagrams it is often convenient
to use conventions which reduce complexity. In this thesis we will occasionally apply
some obvious conventions that need no further explanation.
10.3 Some Properties of Transformation Equivalence
In this section we will give some important and basic propositions of observation equivalence
and transformation equivalence. The proofs of the propositions are given in
Appendix B.
Proposition 3
(i) ¢
(ii) ¢
and ¢
¡
¨
are equivalence relations.
is a weak bisimulation.
Property (i) of Proposition 3 states that both ¢
and ¢
satisfy a minimal set of re-
¡
quirements inherent to any relation pretending to reflect a notion of equivalence. These
requirements are
(1) Reflexivity. Each configuration is equivalent to itself.
(2) Symmetry. If configuration conf p
1 is equivalent to conf p
2 then conf p
2 is equivalent to
conf p
1 .
(3) Transitivity. If configurations conf p
1 and conf p
2 are equivalent and if configuration
conf p
2 and conf p
3 are equivalent then conf p
1 and conf p
3 are also equivalent. Notice that
this property enables the possibility to construct complex behaviour-preserving
transformations from simpler ones.
c
a