Abstract
In this paper we present a refinement operator ·[a ↝ Q], defined both on TCSP-like process terms P and formulas cp of the Modal Mu-Calculus. We show that
the system induced by a term P satisfies a specification φ if and only if the system induced by the refined term P[α ↝ Q] satisfies the refined specification φ[α ↝ Q]
where Q is a process term from an appropriate sublanguage of TCSP. We explain how this result can be used to reason about reactive systems. In particular it supplies a method to verify systems a priori: Provided P ╞ φ holds, the refinement of φ into φ[a ↝ Q] induces a transformation of P into P[a ↝ Q] such that P[a ↝ Q] ╞ φ[a ↝ Q]. The above result holds under the restriction that the set of actions that occur in the term Q has to be disjoint from the set of actions occurring in the term P and the formula φ. Though such restrictions on alphabet disjointness are commonly adopted in approaches to syntactic action refinement for process term languages they preclude the possibility to carry out certain refinement steps that might be necessary in the stepwise development of reactive systems. We show, that while dropping the above restriction, the validity of the two implications comprised in the above result can still be established independently for different interesting fragments of the Modal Mu-Calculus.
The original version of this chapter was revised: The copyright line was incorrect. This has been corrected. The Erratum to this chapter is available at DOI: 10.1007/978-0-387-35533-7_26
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Majster-Cederbaum, M., Salger, F., Sorea, M. (2000). A Priori Verification of Reactive Systems. In: Bolognesi, T., Latella, D. (eds) Formal Methods for Distributed System Development. PSTV FORTE 2000 2000. IFIP — The International Federation for Information Processing, vol 55. Springer, Boston, MA. https://doi.org/10.1007/978-0-387-35533-7_3
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