Specifying & verifying concurrent systems using Z
At present, few guidelines exist for applying the Z notation to concurrent systems, while existing approaches to proving properties of Z specifications of concurrent systems place emphasis on the use of additional formalisms such as temporal logic. This paper proposes a practical and rigorous approach to specifying and verifying concurrent systems using the Z notation alone. Guidelines are given for specifying common features of concurrent systems in Z. A simple lift controller systems is then specified. Finally, a formal proof method based on a simple (weak) fairness rule is presented and is illustrated by means of proofs of safety and liveness properties of the lift controller system.
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- 1.Spivey J.M., The Z Notation (2nd Edition), Prentice Hall, 1993.Google Scholar
- 2.Duke R. et al., Protocol Specification and Verification Using Z, Protocol Specification, Testing and Verification VIII, North Holland 1988, p 33–46.Google Scholar
- 3.Fergus E. and Ince D., Z Specifications and Modal Logic, Proceedings of Software Engineering 90, Brighton, Ed. Patrick Hall, Cambridge University Press, July 1990.Google Scholar
- 4.Lamport, L., 'TLZ', Proceedings of the 8th Z Users Meeting, Cambridge, Springer Verlag, 1994.Google Scholar
- 5.Woodcock J.C.P and Morgan C., Refinement of State-Based Concurrent Systems, Procs. of VDM 90, Springer Verlag, p 341–351, 1990.Google Scholar
- 6.Chandy K.M and Misra J., Parallel Program Design, Addison Wesley, 1988.Google Scholar
- 7.Shankar A.U and Lam.S.S., Time Dependent Distributed Systems: proving safety, liveness and real-time properties, Distributed Computing 2, p 61–79, Springer Verlag, 1987.Google Scholar
- 8.Tel G., Topics In Distributed Algorithms, Cambridge University Press, Chapter 3, 1991.Google Scholar
- 9.Hoare, C.A.R., Communicating Sequential Processes, Prentice Hall, 1985.Google Scholar
- 10.Jackson, M.A., System Development, Prentice Hall International Series in Computer Science, 1983.Google Scholar
- 11.Lamport L., A Simple Approach to Specifying Concurrent Systems, CACM, 32, p 32–45, 1989.Google Scholar
- 12.Evans, A.S., Visualising Concurrent Z Specifications, Proceedings of the 8th Z Users Meeting, Springer Verlag, Cambridge, June 1994.Google Scholar