Abstract
Among the possible approaches for expressing real-time problems with the B method, two are dominant : the use of the usual B mechanisms to define real-time constraints on the one hand, and extending B through another formalism more adapted to the real-time context on the other hand.
We define here a possible real-time semantic for B, by using a real-time logic (the duration calculus), and we illustrate how this extension affects the proof mechanism used to show the soundness of abstract machines.
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References
Abrial, J.-R.: The B Book - Assigning Programs to Meanings. Cambridge University Press, Cambridge (1996)
Abrial, J.-R.: Event driven sequential program construction. École Jeunes chercheurs en programmation (March 2000)
Behm, P., Benoit, P., Faivre, A., Meynadier, J.-M.: METEOR: A successful application of B in a large project. In: Wing, et al. (eds.) [WWD 1999], pp. 369–387
Bodeveix, J.-P., Filali, M.: Machines virtuelles pour le B événementiel. In: AFADL 2003 [IRI03], pp. 227–242
Heitmeyer, C.L., Labaw, B.G., Jeffords, R.D.: A benchmark for comparing different approaches for specifying and verifying real-time systems. In: Tenth IEEE Workshop on Real-Time Operating Systems and Software. IEEE Computer Society Press, Los Alamitos (1993), http://chacs.nrl.navy.mil/personnel/heitmeyer.html
Colin, S., Mariano, G., Poirriez, V.: A natural extension of B substitutions: postconditions. Technical report, LAMIH/ROI (2004), http://www.univ-valenciennes.fr/ROAD/WP/
Colin, S., Poirriez, V., Mariano, G.: Thoughts about the implementation of the duration calculus with coq. In: 4th International Workshop on the Implementation of Logics, volume Technical report ULCS-03-018, University of Liverpool (September 2003), http://www.csc.liv.ac.uk/research/techreports/
Dutertre, B.: Complete proof systems for first order interval temporal logic. In: Logic in Computer Science, pp. 36–43 (1995)
Hammad, A., Julliand, J., Mountassir, H., Ossami, D.O.: Expression en B et raffinement des sytèmes réactifs temps réel. In: AFADL 2003 [IRI03], pp. 211–226 (2003)
Hansen, M.R., Zhou, C.C.: Duration Calculus, a formal approach to real-time systems. Monographs in Theoretical Computer Science. An EATCS Series. Springer, Heidelberg (2004), ISBN: 3-540-40823-1
IRISA. Approches Formelles dans l’Assistance au Développement de Logiciels, IRISA Rennes – France, IRISA (January 2003)
Jianhua, Z., Hung, D.V.: Checking timed automata for some discretisable duration properties. Journal of Computer Science and Technology 15, 423–429 (2000)
Lanet, J.-L.: Using the B method to model protocols. In: AFADL 1998 [LIS98], pp. 79–90 (1998)
Lano, K., Fiadeiro, J., Dick, J.: Extending B AMN with concurrency. Technical report, Dept. of Computing, Imperial College (1996)
LISI/ENSMA. Approches Formelles dans l’Assistance au Développement de Logiciels, Téléport2 - Avenue 1 - BP109 - 86960 FUTUROSCOPE Cedex, LISI/ENSMA (October 1998)
Marcano, R., Levy, N.: Using B formal specifications for analysis and verification of UML/OCL models. In: Workshop on consistency problems in UML-based software development. 5th International Conference on the Unified Modeling Language, Dresden, Germany (September 2002)
Naijun, Z.: Another formal proof for deadline driven scheduler. Technical Report 169, UNU/IIST, P.O. Box 3058, Macau (August 1999)
Pandya, P.K.: Specifying and deciding quantified discrete-time duration calculus formulae using dcvalid. In: RT-TOOLS 2001, Aalborg (August 2001) (affiliated with CONCUR 2001). Technical report TCS-00-PKP-1, Tata Institute of Fundamental Research, Mumbai (2000)
Petit, D.: Génération automatique de composants logiciels sûrs à partir de spécifications formelles B. Thèse de doctorat, Université de Valenciennes et du Hainaut-Cambrésis (December 2003)
Rasmussen, T.M.: Interval Logic - Proof Theory and Theorem Proving. PhD thesis, Informatics and Mathematical Modeling, Technical University of Denmark (January 2002)
Siewe, F., Van Hung, D.: Deriving real-time programs from duration calculus specifications. In: Margaria, T., Melham, T.F. (eds.) CHARME 2001. LNCS, vol. 2144, pp. 92–97. Springer, Heidelberg (2001)
Treharne, H., Schneider, S.: Capturing timing requirements formally in AMN. Technical Report CSD-TR-99-06, Royal Holloway, Department of Computer Science. University of London, Egham, Surrey TW20 0EX, England (June 1999)
Woodcock, J.C.P., Davies, J., Wing, J.M. (eds.): FM 1999. LNCS, vol. 1709, p. 1861. Springer, Heidelberg (1999)
Zhou, C.C., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Information Processing Letters 10(5), 269–276 (1991)
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Colin, S., Mariano, G., Poirriez, V. (2005). Duration Calculus: A Real-Time Semantic for B. In: Liu, Z., Araki, K. (eds) Theoretical Aspects of Computing - ICTAC 2004. ICTAC 2004. Lecture Notes in Computer Science, vol 3407. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-31862-0_31
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