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International Conference of B and Z Users

ZB 2005: ZB 2005: Formal Specification and Development in Z and B pp 24–44Cite as

Non-atomic Refinement in Z and CSP

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Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 3455))

Abstract

In this paper we discuss the relationship between notions of non-atomic (or action) refinement in a state-based setting with that in a behavioural setting. In particular, we show that the definition of non-atomic coupled downward simulation as defined for Z and Object-Z is sound with respect to an action refinement definition of CSP failures refinement.

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References

  1. Aceto, L.: Action Refinement in Process Algebras. CUP, London (1992)

    Google Scholar 

  2. Boiten, E.A., Derrick, J.: IO-refinement in Z. In: Evans, A., Duke, D.J., Clark, T. (eds.) 3rd BCS-FACS Northern Formal Methods Workshop, September 1998. Springer, Heidelberg (1998), http://www.ewic.org.uk/

    Google Scholar 

  3. Bolton, C., Davies, J.: A Singleton Failures Semantics for Communicating Sequential Processes. In: Formal Aspects of Computing. Under consideration (2002)

    Google Scholar 

  4. Bolton, C., Davies, J.: Refinement in Object-Z and CSP. In: Butler, M., Petre, L., Sere, K. (eds.) IFM 2002. LNCS, vol. 2335, pp. 225–244. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  5. Derrick, J., Boiten, E.: Non-atomic refinement in Z. In: Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.) FM 1999. LNCS, vol. 1709, pp. 1477–1496. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  6. Derrick, J., Boiten, E.A.: Refinement in Z and Object-Z. Springer, Heidelberg (2001)

    MATH  Google Scholar 

  7. Derrick, J., Boiten, E.A.: Relational concurrent refinement. Formal Aspects of Computing 15(2-3), 182–214 (2003)

    Article  MATH  Google Scholar 

  8. Derrick, J., Wehrheim, H.: Using coupled simulations in non-atomic refinement. In: Bert, D., P. Bowen, J., King, S. (eds.) ZB 2003. LNCS, vol. 2651, pp. 127–147. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  9. Fischer, C.: CSP-OZ - a combination of CSP and Object-Z. In: Bowman, H., Derrick, J. (eds.) Second IFIP International conference on Formal Methods for Open Object-based Distributed Systems, July 1997, pp. 423–438. Chapman & Hall, Boca Raton (1997)

    Google Scholar 

  10. Fischer, C.: How to combine Z with a process algebra. In: P. Bowen, J., Fett, A., Hinchey, M.G. (eds.) ZUM 1998. LNCS, vol. 1493, pp. 5–23. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  11. Galloway, A., Stoddart, W.: An operational semantics for ZCCS. In: Hinchey, M.G., Liu, S. (eds.) First International Conference on Formal Engineering Methods (ICFEM 1997), Hiroshima, Japan, November 1997, pp. 272–282. IEEE Computer Society Press, Los Alamitos (1997)

    Chapter  Google Scholar 

  12. He, J.: Process simulation and refinement. Formal Aspects of Computing 1, 229–241 (1989)

    Article  Google Scholar 

  13. Janssen, W., Poel, M., Zwiers, J.: Actions systems and action refinement in the development of parallel systems. In: Groote, J.F., Baeten, J.C.M. (eds.) CONCUR 1991. LNCS, vol. 527, pp. 298–316. Springer, Heidelberg (1991)

    Google Scholar 

  14. Jifeng, H.: Process refinement. In: McDermid, J. (ed.) The Theory and Practice of Refinement, Butterworths (1989)

    Google Scholar 

  15. Josephs, M.B.: A state-based approach to communicating processes. Distributed Computing 33, 9–18 (1988)

    Article  Google Scholar 

  16. Mahony, B.P., Dong, J.S.: Blending Object-Z and timed CSP: An introduction to TCOZ. In: Futatsugi, K., Kemmerer, R., Torii, K. (eds.) 20th International Conference on Software Engineering (ICSE 1998). IEEE Press, Los Alamitos (1998)

    Google Scholar 

  17. Parrow, J., Sjödin, P.: Multiway Synchronisation Verified with Coupled Simulation. In: Cleaveland, W.R. (ed.) CONCUR 1992. LNCS, vol. 630, pp. 518–533. Springer, Heidelberg (1992)

    Chapter  Google Scholar 

  18. Rensink, A.: Action Contraction. In: Palamidessi, C. (ed.) CONCUR 2000. LNCS, vol. 1877, pp. 290–304. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  19. Rensink, A., Wehrheim, H.: Dependency-based action refinement. In: Privara, I., Ružička, P. (eds.) MFCS 1997. LNCS, vol. 1295. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  20. Roscoe, A.W.: The Theory and Practice of Concurrency (1998)

    Google Scholar 

  21. Smith, G., Derrick, J.: Specification, refinement and verification of concurrent systems - an integration of Object-Z and CSP. Formal Methods in Systems Design 18, 249–284 (2001)

    Article  MATH  Google Scholar 

  22. Stepney, S., Cooper, D., Woodcock, J.C.P.: More powerful data refinement in Z. In: Bowen, J. P., Fett, A., Hinchey, M.G. (eds.) ZUM 1998. LNCS, vol. 1493, pp. 284–307. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  23. Treharne, H., Schneider, S.: Using a process algebra to control B operations. In: Araki, K., Galloway, A., Taguchi, K. (eds.) International Conference on Integrated Formal Methods 1999 (IFM 1999), York, July 1999, pp. 437–456. Springer, Heidelberg (1999)

    Google Scholar 

  24. van Glabbeek, R., Goltz, U.: Equivalence notions for concurrent systems and refinement of actions. In: Kreczmar, A., Mirkowska, G. (eds.) MFCS 1989. LNCS, vol. 379, pp. 237–248. Springer, Heidelberg (1989)

    Google Scholar 

  25. Woodcock, J.C.P., Davies, J.: Using Z: Specification, Refinement, and Proof. Prentice Hall, Englewood Cliffs (1996)

    MATH  Google Scholar 

  26. Woodcock, J.C.P., Morgan, C.C.: Refinement of state-based concurrent systems. In: Langmaack, H., Hoare, C.A.R., Bjorner, D. (eds.) VDM 1990. LNCS, vol. 428. Springer, Heidelberg (1990)

    Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Computing, University of Sheffield, Sheffield, UK

    John Derrick

  2. Institut für Informatik, Universität Paderborn, 33098, Paderborn, Germany

    Heike Wehrheim

Authors
  1. John Derrick
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  2. Heike Wehrheim
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Editor information

Editors and Affiliations

  1. Department of Computing, University of Surrey,  

    Helen Treharne  & Steve Schneider  & 

  2. Department of Computer Science, University of York, P.O. Box, YO10 5DD, Heslington, York, UK

    Steve King

  3. Department of Computer Science, University of Essex, P.O. Box, UK

    Martin Henson

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Derrick, J., Wehrheim, H. (2005). Non-atomic Refinement in Z and CSP. In: Treharne, H., King, S., Henson, M., Schneider, S. (eds) ZB 2005: Formal Specification and Development in Z and B. ZB 2005. Lecture Notes in Computer Science, vol 3455. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11415787_3

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  • DOI: https://doi.org/10.1007/11415787_3

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-25559-8

  • Online ISBN: 978-3-540-32007-4

  • eBook Packages: Computer ScienceComputer Science (R0)

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