PSTV 2000, FORTE 2000: Formal Methods for Distributed System Development pp 35-50

# A Priori Verification of Reactive Systems

On Simultaneous Syntactic Action Refinement for TCSP and the Modal Mu-Calculus
• Mila Majster-Cederbaum
• Frank Salger
• Maria Sorea
Chapter
Part of the IFIP — The International Federation for Information Processing book series (IFIPAICT, volume 55)

## Abstract

In this paper we present a refinement operator ·[aQ], 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[αQ] satisfies the refined specification φ[αQ]

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 Pφ holds, the refinement of φ into φ[aQ] induces a transformation of P into P[aQ] such that P[aQ] ╞ φ[aQ]. 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.

## Keywords

Verification Syntactic Action Refinement Process Algebra Reactive Systems Temporal Logic.

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© IFIP International Federation for Information Processing 2000

## Authors and Affiliations

• Mila Majster-Cederbaum
• 1
• Frank Salger
• 1
• Maria Sorea
• 1
1. 1.Fakultät für Mathematik und Informatik, D7, 27Universität MannheimMannheimGermany