Abstract
We present a stepwise formal development of the Peterson’s mutual exclusion algorithm using Event B. We use a bottom-up approach where we introduce the parallel composition of subsystems which are separately specified. First, we specify subsystems as B abstract systems; then we compose the subsystems to get a first abstract solution for the mutual exclusion. This solution is improved to obtain the Peterson’s algorithm. This is achieved by refinement and composition of the former abstract subsystems. Therefore the result is formally proved on the basis of correctness (safety) properties added to the invariant. Atelier B (a B prover) is used to check completely the development.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Abrial, J.-R.: The B Book. Cambridge University Press, Cambridge (1996)
Abrial, J.-R.: Extending B without Changing it (for developping distributed systems). In: Habrias, H. (ed.) Proc. of the 1st Conference on the B method, France, pp. 169–190 (1996)
Abrial, J.-R.: Event Driven Distributed Program Construction. MATISSE project (August 2001)
Abrial, J.-R.: Discrete System Models. Internal Notes ( B, B Working Group) (February 2002), available at http://www-lsr.imag.fr/
Abrial, J.-R., Cansell, D., Mery, D.: Formal Derivation of Spanning Trees Algorithms. In: Bert, D., P. Bowen, J., King, S. (eds.) ZB 2003. LNCS, vol. 2651, pp. 457–476. Springer, Heidelberg (2003)
Abrial, J.-R., Mussat, L.: Introducing Dynamic Constraints in B. In: Bert, D. (ed.) B 1998. LNCS, vol. 1393, pp. 83–128. Springer, Heidelberg (1998)
Attiogbé, C.: A Mechanically Proved Development Combining B Abstract Systems and Spin. In: Proceedings of the 4th International Conference on Quality Software (QSIC 2004). IEEE Computer Society Press, Los Alamitos (2004)
Attiogbé, C.: Communicating B Abstract Systems (CBS). Technical Report 02.08, IRIN, University of Nantes (December 2002)
Back, R.J., Sere, K.: From Action Systems to Modular Systems. Software - Concepts and Tools 17(1), 26–39 (1996)
Back, R.-J., Wright, J.V.: Refinement Calculus: A Systematic Introduction. Graduate Texts in Computer Science. Springer, Heidelberg (1998)
Back, R.J.R., Butler, M.J.: Fusion and Simultaneous Execution in the Refinement Calculus. Acta Informatica 35(11), 921–949 (1998)
Back, R.J., Kurki-Suonio, R.: Decentralisation of Process Nets with Centralised Control. In: Proc. of the 2nd ACM SIGACT-SIGOPS Symposium on Principles of Distributed Computing, pp. 131–142. ACM, New York (1983)
Bert, D., Bowen, J.P., Henson, M.C., Robinson, K. (eds.): ZB 2002: Formal Specification and Development in Z and B, 2nd International Conference of B and Z Users, France. LNCS, vol. 2272. Springer, Heidelberg (2002)
Bert, D., Potet, M.-L., Rouzaud, Y.: A Study on Components and Assembly Primitives in B. In: Habrias, H. (ed.) Proc. of the 1st Conference on the B method, France, November 1996, pp. 47–62 (1996)
Butler, M., Walden, M.: Distributed System Development in B. In: Habrias, H. (ed.) Proc. of the 1st Conference on the B method, France, pp. 155–168 (1996)
Butler, M.J.: Stepwise Refinement of Communicating Systems. Science of Computer Programming 27(2), 139–173 (1996)
ClearSy. Atelier, B.: V3.6. Steria, Aix-en-Provence, France
Dunne, S.: The Safe Machine: A New Specification Construct for B. In: Proceedings of FM 1999: World Congress on Formal Methods, pp. 472–489 (1999)
Dunne, S.: A Theory of Generalised Substitutions. In: Bert et al.[13]. pp. 270–290
Hoare, C.A.R.: Communicating Sequential Processes. Prentice-Hall, Englewood Cliffs (1985)
Kesten, Y., Manna, Z., Pnueli, A.: Temporal Verification of Simulation and Refinement. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1993. LNCS, vol. 803, pp. 273–346. Springer, Heidelberg (1994)
MATISSE. Handbook for Correct Systems Construction. Technical Report IST-1999-11345, EU-Project MATISSE: Methodologies and Technoloies for Industrial Strength Systems Engineering,University of Southampton (April 2003)
Schneider, S., Treharne, H.: Verifying Controlled Components. In: Boiten, E.A., Derrick, J., Smith, G.P. (eds.) IFM 2004. LNCS, vol. 2999, pp. 87–107. Springer, Heidelberg (2004)
Schneider, S., Treharne, H.: Communicating B Machines. In: Bert, et al. [13], pp. 416–435
Xu, Q.: On Compositionality in Refining Concurrent Systems. In: He, J., Cooke, J., Wallis, P. (eds.) Proceedings of the BCS FACS 7th Refinement Workshop. Springer, Heidelberg (1996)
Xu, Q., de Roever, W.P., He, J.: The Rely-Guarantee Method for Verifying Shared Variable Concurrent Programs. Formal Aspects of Computing 9(2), 149–174 (1997)
Xu, Q., Swarup, M.: Compositional Reasoning Using the Assumption-Commitment Paradigm. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 565–583. Springer, Heidelberg (1998)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Attiogbé, J.C. (2005). A Stepwise Development of the Peterson’s Mutual Exclusion Algorithm Using B Abstract Systems. 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_8
Download citation
DOI: https://doi.org/10.1007/11415787_8
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)