Factorization of finite state machines under observational equivalence

Abstract

A usual approach to designing a complex concurrent system is to follow the topdown design methodology: the abstract specification of the system is decomposed into a network of communicating modules such that the behavior of the modules in composition is equivalent to the behavior of the system specification.

The factorization problem is to construct the specification of a submodule X when the specifications of the system and all submodules but X are given. It is usually described by the equaition $A|X\mathop = \limits^e B$ where A and X are submodules of system B, | is a composition operator, and $\mathop = \limits^e$ is the equivalence criterion.

In this paper we use a finite state machine (FSM) model consistent with CCS and study the factorization problem $A|||X \approx B$ where ||| is a derived CCS composition operator and ≈ represents observational equivalence. An algorithm is presented and proved correct to find the most general specification of submodule X for $A|||X \approx B$ with B deterministic. This paper extends and is based on the work of M.W. Shields.

Partially supported by the National Science Foundation under grant number CCR8822839