Linear Temporal Logic and Z Refinement
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.
KeywordsZ refinement temporal logic LTL
Unable to display preview. Download preview PDF.
- 2.Bolton, C., Davies, J.: A Singleton Failures Semantics for Communicating Sequential Processes. Formal Aspects of Computing (2002) (under consideration)Google Scholar
- 4.Clarke, E., Grumberg, O., Peled, D.: Model Checking. MIT Press, Cambridge (2000)Google Scholar
- 8.Emerson, E.A.: Temporal and modal logic. In: van Leeuwen, J. (ed.) Handbook of Theoretical Computer Science, vol. B, pp. 996–1072. Elsevier Science Publishers, Amsterdam (1990)Google Scholar
- 11.Loiseaux, C., Graf, S., Sifakis, J., Bouajjani, A., Bensalem, S.: Property preserving abstractions for the verification of concurrent systems. Formal Methods in System Design 6(1) (1995)Google Scholar
- 12.Smith, G.: The Object-Z Specification Language. In: Smith, G. (ed.) Advances in Formal Methods, Kluwer Academic Publishers, Dordrecht (2000)Google Scholar
- 14.Spivey, J.M.: The Z Notation: A Reference Manual, 2nd edn. Prentice Hall, Englewood Cliffs (1992)Google Scholar