Abstract
The factorisation problem is to construct the specification of a submoduleX when the specifications of the system and all submodules butX are given. It is usually described by the equation\(P|X\mathop = \limits^e Q\) where P and X are submodules of system Q, ¦ 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 two factorisation problems:P |||P ∼Q andP |||P ≈Q, where ||| is a derived CCS composition operator, ∼ and ≈ represent strong and observational equivalences. Algorithms are presented and proved correct to find the most general specification of submoduleX forP |||P ∼Q withQ τ-deterministic and forP |||P ≈Q withQ deterministic. Conditions on the submachines of the most general solutions that remain solutions toP |||P ∼Q(P |||P ≈Q) are given. This paper extends and is based on the work of M. W. Shields.
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Qin, H., Lewis, P. Factorisation of finite state machines under strong and observational equivalences. Formal Aspects of Computing 3, 284–307 (1991). https://doi.org/10.1007/BF01245634
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DOI: https://doi.org/10.1007/BF01245634