Developing a design framework for communication systems

ion: Specification (V) resulted at the end of step 2. It specifies the same behaviour as (III). As (111) is the specification that resulted at the end of step 1, this suggests that no progress is made in the design. To distinguish between the two expressions an operator is needed that allows you to mark the boundary in an expression between the design decisions made and the design decisions to he made. Such an operator is now added to the notation. This new operator abstracts from certain aspects in a specification. Therefore, it is called an abstraction operator. The operator is denoted by: '•'. It has an expression on the left-hand side and a set of action symbols on the right-hand side. E•B denotes the behaviour of expression E with respect to the action symbols in B. The other action symbols are just a means to obtain this behaviour. They are not part of that what has to he designed. Only their effect on the ordering of action symbols in B is important. Furthermore, this expression abstracts from structural constraints on systems that provide the behaviour. It does not specify a number of subsystems that interact with each other to provide this behaviour. At this stage of the design, the specified system is a black box (hence the symbol used to denote the abstraction operator) with behaviour. Assume that E•B is detailed into El•Bl 11 E2•B2. This expression specifies that the system has to consist of two subsystems in parallel. The behaviour of one subsystem is specified by El•Bl and the behaviour of the other is specified by E2•B2. These subsystems have to he detailed in future detailing steps. In ACP, CSP, and LOTOS this type of abstraction operator does not occur. As these languages only focus on behaviour, their abstraction operator only abstracts from action symbols. CCS has a parallel operator that abstracts from the identity of interactions. As far as we know, the abstraction operator used in this thesis is first presented in [Hui91]. Applying this operator to (IV) yields the following integrated specification: ((w; x; y; z; T)•{w,x, y, x})l{w,x, y,x} with T w; x; y; z;T ~· (((w;x;y; z; T)•{w,x,y,x})f{w,x,y,x}) = 0 Applying this operator to (V) yields the following specification: (E 11 (S•{w,x,y,z})H{w,x,y,z} with E = w; E + x; E + y; E + z; E f!. E = {w,x,y, z} S = w;x;y;z;S ~.S= {w,x,y,x,z} (VI)