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

316 Behaviour-Preserving Transformations
c
A B
a
b
c
d
a
¡
¢
¡
c
A B
The reason is that the specification of the left-hand side of the picture allows communication
between A and B over channel b, whereas the right-hand side does not allow any
communication between the two parties!
Transformation 12
e p
envs¥ BSpec Sys ¥ Sys
¥ 1
¢
¡
e p
envs¥ BSpec Sys ¥ Sys
¥ 2
if Sys p
1 and Sys p
2 are non-conflicting ¨
Two systems of process and cluster classes Sys p
1
a
and Sysp
2
if for every class name occurring in Sys p
1 as well as Sys p
tions are syntactically identical.
b
b
c
are defined to be non-conflicting
2, the corresponding class defini-
By 12 it is allowed to add a new class or to remove an existing class from a system of
process and cluster classes Sys p contained in some configuration conf p . Note, however,
that the resulting configuration, say conf p ¡ , must be a valid one, i.e. that conf p ¡ ¡ Conf p .
In the case conf p ¡ is a system specification, this means that it has to conform to all the
context conditions as defined in Subsection 9.4.
Transformation 13
(i) C c (E1 ¥¡ ¡ ¡ ¥ Er)¥
p
§ § E1© BSpec ¥¡ ¡ ¡ ¥ Er© Pr ¥
P1
if Cc denotes the name of a cluster class defined in Sysp by
¥ Sys p ¥ Sys
cluster class Cc ¡ ¥ Pr ¥¡ ¡
¡ ¡
P1
communication channels ch1 chk
message interface la 1 ¡ ¡ la behaviour specification
l
BSpecp ¢
¡
d
a
¥ Sys p Sys ¥
(ii)
§ BSpece Cc ¡ ¡£ Er¢ ¥ envs¥ Sys E1£ ¡ p ¢
¡
e BSpec ¥ envs¥ p Sys ¥ Sys
¥ Sys
if Cc is defined in a similar way as in (i) and if Reset(BSpece )
BSpecp E1© P1 ¥¡ ¡ ¡ ¥ Er © Pr . ¨
§ §
Transformation 13 states that the collaborating behaviour of the instances from which a
cluster instance is constituted is equivalent to the behaviour of the cluster instance itself.
It is therefore allowed to replace any cluster by the system of instances from which it is
constituted. On the other hand any system of collaborating instances can be combined
into an appropriate cluster instance, thereby introducing an extra hierarchical level in the
corresponding system specification. Clustering a system of instances may involve the