Proving Temporal Properties of Z Specifications Using Abstraction

Smith, Graeme; Winter, Kirsten

doi:10.1007/3-540-44880-2_17

Cited by 14 publications

(27 citation statements)

References 19 publications

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“…Although soundness is not formally verified, it is fairly evident as we exploit natural similarities between state based specification in Object-Z and the state model of SMV. The integration of temporal logics and Object-Z semantics is furthermore based on well-established results [3], [15].…”

Section: Conclusion and Discussionmentioning

confidence: 99%

Formal Methods for Industrial Critical Systems

Lang

Flammini

2008

Lecture Notes in Computer Science

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Abstract. In the context of large scale industrial installations, model checking often fails to tap its full potential because of a missing link between a system's specification and its functional and non-functional requirements, like safety. Our work bridges this gap by providing a translation from the formal specification language Object-Z to the SMV model checker input language to combine their advantages. This paper focuses on the translation of the object-oriented features of Object-Z: operation promotion and communication between objects. We demonstrate the feasibility of our approach using the example of the TWIN Elevator system and embed the translation process in the industrial software production workflow.

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Section: Conclusion and Discussionmentioning

confidence: 99%

Formal Methods for Industrial Critical Systems

Lang

Flammini

2008

Lecture Notes in Computer Science

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“…An abstraction relation over temporal structures maps an infinite structure to a finite (more abstract) one which preserves the properties to be shown. The work by Smith and Winter [SW03] introduces such an abstraction technique for Z. Future work will investigate how this abstraction technique can be adapted for Object-Z and how it can be combined with our compositional proof strategy.…”

Section: Discussionmentioning

confidence: 99%

“…Inputs and output variables are embedded into the state space following the approach of Smith and Winter [SW03]. Special variables are included in the state to denote the component and sub-component events which occurred in the transition to the current state.…”

Section: A Z Specification Of Oz Structuresmentioning

confidence: 99%

Compositional Verification for Object-Z

Winter

Smith

2003

ZB 2003: Formal Specification and Development in Z and B

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Abstract. This paper presents a framework for compositional verification of Object-Z specifications. Its key feature is a proof rule based on decomposition of hierarchical Object-Z models. For each component in the hierarchy local properties are proven in a single proof step. However, we do not consider components in isolation. Instead, components are envisaged in the context of the referencing super-component and proof steps involve assumptions on properties of the sub-components. The framework is defined for Linear Temporal Logic (LTL).

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“…This can be done as detailed in [13]. In brief, the type of each input and output when embedded in the state is extended with a value ⊥ and this value is used for the pre-state value of embedded inputs and post-state value of embedded outputs when they are not declared in a particular schema of the original specification.…”

Section: Temporal Structuresmentioning

confidence: 99%

“…Hence, investigating their use with Z is an important first step toward developing model checking support for the language [13]. The most common temporal logics used in model checking are Linear Temporal Logic (LTL) [8], Computation Tree Logic (CTL) [8] and the µ-calculus [10].…”

Section: Introductionmentioning

confidence: 99%

Linear Temporal Logic and Z Refinement

Derrick

Smith

2004

Algebraic Methodology and Software Technology

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Abstract. Since Z, being a state-based language, describes a system in terms of its state and potential state changes, it is natural to want to describe properties of a specified system also in terms of its state. One means of doing this is to use Linear Temporal Logic (LTL) in which properties about the state of a system over time can be captured. This, however, raises the question of whether these properties are preserved under refinement. Refinement is observation preserving and the state of a specified system is regarded as internal and, hence, non-observable. In this paper, we investigate this issue by addressing the following questions. Given that a Z specification A is refined by a Z specification C , and that P is a temporal logic property which holds for A, what temporal logic property Q can we deduce holds for C ? Furthermore, under what circumstances does the property Q preserve the intended meaning of the property P ? The paper answers these questions for LTL, but the approach could also be applied to other temporal logics over states such as CTL and the µ-calculus.

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Proving Temporal Properties of Z Specifications Using Abstraction

Cited by 14 publications

References 19 publications

Formal Methods for Industrial Critical Systems

Formal Methods for Industrial Critical Systems

Compositional Verification for Object-Z

Linear Temporal Logic and Z Refinement

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