Submodule Construction Using Derivatives

Top-down design methodology is one of the widely used approaches to the design of complex concurrent systems. In this approach, the speciication of a system is decomposed into a set of submodules whose concurrent behavior is equivalent to that of the system speciication. The following problem is of particular importance when using this methodology: given the speciication of a system and some of its submodules, derive a speciication for the remaining submodules. This problem can be formulated in CCS as Ak L X B where \k L " is the combination of CCS operators composition and restriction, A is the composition of all known submodules, X is the unknown submodule, B represents the entire system and L represents the actions that may be used for communication between submodules. This paper presents an algorithm for the solution of Ak L X B where B is deterministic. The proposed algorithm uses the concept of derivatives. The use of the algorithm is demonstrated by several examples.