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Analysis of Linear Hybrid Systems in CLP

  • Conference paper
Logic-Based Program Synthesis and Transformation (LOPSTR 2008)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 5438))

Abstract

In this paper we present a procedure for representing the semantics of linear hybrid automata (LHAs) as constraint logic programs (CLP); flexible and accurate analysis and verification of LHAs can then be performed using generic CLP analysis and transformation tools. LHAs provide an expressive notation for specifying real-time systems. The main contributions are (i) a technique for capturing the reachable states of the continuously changing state variables of the LHA as CLP constraints; (ii) a way of representing events in the LHA as constraints in CLP, along with a product construction on the CLP representation including synchronisation on shared events; (iii) a framework in which various kinds of reasoning about an LHA can be flexibly performed by combining standard CLP transformation and analysis techniques. We give experimental results to support the usefulness of the approach and argue that we contribute to the general field of using static analysis tools for verification.

Work partly supported by the Danish Natural Science Research Council project SAFT: Static Analysis Using Finite Tree Automata.

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References

  1. Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.-H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995)

    Article  MathSciNet  MATH  Google Scholar 

  2. Alur, R., Courcoubetis, C., Henzinger, T.A., Ho, P.-H.: Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In: Grossman, R.L., Ravn, A.P., Rischel, H., Nerode, A. (eds.) HS 1991 and HS 1992. LNCS, vol. 736, pp. 209–229. Springer, Heidelberg (1993)

    Chapter  Google Scholar 

  3. Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  4. Bagnara, R., Hill, P.M., Zaffanella, E.: Widening operators for powerset domains. J. Software Tools for Technology Transfer 8(4-5), 449–466 (2006)

    Article  MATH  Google Scholar 

  5. Bagnara, R., Ricci, E., Zaffanella, E., Hill, P.M.: Possibly not closed convex polyhedra and the Parma Polyhedra Library. In: Hermenegildo, M.V., Puebla, G. (eds.) SAS 2002. LNCS, vol. 2477, pp. 213–229. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  6. Behrmann, G., David, A., Larsen, K.G.: A tutorial on Uppaal. In: Bernardo, M., Corradini, F. (eds.) SFM-RT 2004. LNCS, vol. 3185, pp. 200–236. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  7. Benoy, F., King, A.: Inferring argument size relationships with CLP(R). In: Gallagher, J.P. (ed.) LOPSTR 1996. LNCS, vol. 1207, pp. 204–223. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

  8. Brzoska, C.: Temporal logic programming in dense time. In: ILPS, pp. 303–317. MIT Press, Cambridge (1995)

    Google Scholar 

  9. Carloni, L.P., Passerone, R., Pinto, A., Sangiovanni-Vincentelli, A.L.: Languages and tools for hybrid systems design. Found. Trends Electron. Des. Autom. 1(1/2), 1–193 (2006)

    Article  MATH  Google Scholar 

  10. Codish, M., Taboch, C.: A semantic basic for the termination analysis of logic programs. The Journal of Logic Programming 41(1), 103–123 (1999)

    Article  MATH  Google Scholar 

  11. Cousot, P., Halbwachs, N.: Automatic discovery of linear restraints among variables of a program. In: Proceedings of the 5th Annual ACM Symposium on Principles of Programming Languages, pp. 84–96 (1978)

    Google Scholar 

  12. Debray, S., Ramakrishnan, R.: Abstract Interpretation of Logic Programs Using Magic Transformations. Journal of Logic Programming 18, 149–176 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  13. Delzanno, G., Podelski, A.: Model checking in CLP. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 223–239. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  14. Du, X., Ramakrishnan, C.R., Smolka, S.A.: Real-time verification techniques for untimed systems. Electr. Notes Theor. Comput. Sci. 39(3) (2000)

    Google Scholar 

  15. Fioravanti, F., Pettorossi, A., Proietti, M.: Verifying CTL properties of infinite-state systems by specializing constraint logic programs. In: Leuschel, M., Podelski, A., Ramakrishnan, C., Ultes-Nitsche, U. (eds.) Proceedings of the Second International Workshop on Verification and Computational Logic (VCL 2001), pp. 85–96 (2001); tech. Report DSSE-TR-2001-3, University of Southampton

    Google Scholar 

  16. Gallagher, J.P., Henriksen, K.S.: Abstract domains based on regular types. In: Demoen, B., Lifschitz, V. (eds.) ICLP 2004. LNCS, vol. 3132, pp. 27–42. Springer, Heidelberg (2004)

    Chapter  Google Scholar 

  17. Gallagher, J.P., Henriksen, K.S., Banda, G.: Techniques for scaling up analyses based on pre-interpretations. In: Gabbrielli, M., Gupta, G. (eds.) ICLP 2005. LNCS, vol. 3668, pp. 280–296. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  18. Genaim, S., Codish, M.: Inferring termination conditions of logic programs by backwards analysis. In: Nieuwenhuis, R., Voronkov, A. (eds.) LPAR 2001. LNCS, vol. 2250, pp. 681–690. Springer, Heidelberg (2001)

    Google Scholar 

  19. Gupta, G., Bansal, A., Min, R., Simon, L., Mallya, A.: Coinductive logic programming and its applications. In: Dahl, V., Niemelä, I. (eds.) ICLP 2007. LNCS, vol. 4670, pp. 27–44. Springer, Heidelberg (2007)

    Chapter  Google Scholar 

  20. Gupta, G., Pontelli, E.: A constraint-based approach for specification and verification of real-time systems. In: IEEE Real-Time Systems Symposium, pp. 230–239 (1997)

    Google Scholar 

  21. Halbwachs, N., Proy, Y.E., Raymound, P.: Verification of linear hybrid systems by means of convex approximations. In: LeCharlier, B. (ed.) SAS 1994. LNCS, vol. 864, pp. 223–237. Springer, Heidelberg (1994)

    Chapter  Google Scholar 

  22. Henriksen, K.S., Banda, G., Gallagher, J.P.: Experiments with a convex polyhedral analysis tool for logic programs. In: Workshop on Logic Programming Environments, Porto (2007)

    Google Scholar 

  23. Henriksen, K.S., Gallagher, J.P.: Abstract interpretation of PIC programs through logic programming. In: Proceedings of SCAM 2006, Sixth IEEE International Workshop on Source Code Analysis and Manipulation (2006)

    Google Scholar 

  24. Henzinger, T.A.: The theory of hybrid automata. In: Clarke, E.M. (ed.) Proceedings, 11th Annual IEEE Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)

    Chapter  Google Scholar 

  25. Jaffar, J., Maher, M.: Constraint Logic Programming: A Survey. Journal of Logic Programming 19/20, 503–581 (1994)

    Google Scholar 

  26. Jaffar, J., Santosa, A.E., Voicu, R.: A CLP proof method for timed automata. In: Anderson, J., Sztipanovits, J. (eds.) The 25th IEEE International Real-Time Systems Symposium, pp. 175–186. IEEE Computer Society, Los Alamitos (2004)

    Chapter  Google Scholar 

  27. Katoen, J.-P.: Concepts, algorithms, and tools for model checking. A lecture notes of the course “Mechanised Validation of Parallel Systems” for 1998/99 at Friedrich-Alexander Universitat, Erlangen-Nurnberg, p. 195 (1999)

    Google Scholar 

  28. Leuschel, M., Fontaine, M.: Probing the depths of CSP-M: A new fdr-compliant validation tool. In: Liu, S., Maibaum, T., Araki, K. (eds.) ICFEM 2008. LNCS, vol. 5256, pp. 278–297. Springer, Heidelberg (2008)

    Google Scholar 

  29. Leuschel, M., Jørgensen, J.: Efficient specialisation in Prolog using the hand-written compiler generator LOGEN. Elec. Notes Theor. Comp. Sci. 30(2) (1999)

    Google Scholar 

  30. Leuschel, M., Massart, T.: Infinite state model checking by abstract interpretation and program specialisation. In: Bossi, A. (ed.) LOPSTR 1999. LNCS, vol. 1817, pp. 63–82. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  31. Mesnard, F.: Towards automatic control for CLP(χ) programs. In: Proietti, M. (ed.) LOPSTR 1995. LNCS, vol. 1048, pp. 106–119. Springer, Heidelberg (1996)

    Chapter  Google Scholar 

  32. Nilsson, U., Lübcke, J.: Constraint logic programming for local and symbolic model-checking. In: Palamidessi, C., Moniz Pereira, L., Lloyd, J.W., Dahl, V., Furbach, U., Kerber, M., Lau, K.-K., Sagiv, Y., Stuckey, P.J. (eds.) CL 2000. LNCS, vol. 1861, pp. 384–398. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  33. Pemmasani, G., Ramakrishnan, C.R., Ramakrishnan, I.V.: Efficient real-time model checking using tabled logic programming and constraints. In: Stuckey, P.J. (ed.) ICLP 2002. LNCS, vol. 2401, pp. 100–114. Springer, Heidelberg (2002)

    Chapter  Google Scholar 

  34. Peralta, J.C., Gallagher, J.P.: Convex hull abstractions in specialization of CLP programs. In: Leuschel, M.A. (ed.) LOPSTR 2002. LNCS, vol. 2664, pp. 90–108. Springer, Heidelberg (2003)

    Chapter  Google Scholar 

  35. Podelski, A.: Model checking as constraint solving. In: Palsberg, J. (ed.) SAS 2000. LNCS, vol. 1824, pp. 22–37. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

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Authors and Affiliations

  1. Roskilde University, Building 43.2, P.O. Box 260, DK-4000, Denmark

    Gourinath Banda & John P. Gallagher

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  1. Gourinath Banda
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  2. John P. Gallagher
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  1. Institut für Informatik, Christian-Albrechts-Universität Kiel, 24098, Kiel, Germany

    Michael Hanus

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Banda, G., Gallagher, J.P. (2009). Analysis of Linear Hybrid Systems in CLP. In: Hanus, M. (eds) Logic-Based Program Synthesis and Transformation. LOPSTR 2008. Lecture Notes in Computer Science, vol 5438. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-00515-2_5

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  • DOI: https://doi.org/10.1007/978-3-642-00515-2_5

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-00514-5

  • Online ISBN: 978-3-642-00515-2

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