Abstract
In this article, we present a model and a denotational semantics for hybrid systems. Our model is designed to be used for the verification of large, existing embedded applications. The discrete part is modeled by a program written in an extension of an imperative language and the continuous part is modeled by differential equations. We give a denotational semantics to the continuous system inspired by what is usually done for the semantics of computer programs and then we show how it merges into the semantics of the whole system. The semantics of the continuous system is computed as the fix-point of a modified Picard operator which increases the information content at each step.
Chapter PDF
Similar content being viewed by others
Keywords
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
References
Alur, R., Grosu, R., Hur, Y., Kumar, V., Lee, I.: Modular specification of hybrid systems in charon. In: Lynch, N.A., Krogh, B.H. (eds.) HSCC 2000. LNCS, vol. 1790, Springer, Heidelberg (2000)
Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O’Hearn, P.: Variance analyses from invariance analyses. In: POPL, pp. 211–224 (2007)
Bouissou, O., Martel, M.: A hybrid denotational semantics of hybrid systems - extended version, http://hal.archives-ouvertes.fr/hal-00177031/
Bouissou, O., Martel, M.: GRKLib: a guaranteed runge-kutta library. In: International Symposium on Scientific Computing, Computer Arithmetic and Validated Numerics, IEEE, Los Alamitos (2006)
Cousot, P.: Integrating physical systems in the static analysis of embedded control software. In: Yi, K. (ed.) APLAS 2005. LNCS, vol. 3780, pp. 135–138. Springer, Heidelberg (2005)
Cousot, P., Cousot, R.: Abstract interpretation: a unified lattice model for static analysis of programs by construction or approximation of fixpoints. In: POPL, pp. 238–252. ACM Press, New York (1977)
Cousot, P., Cousot, R., Feret, J., Mauborgne, L., Monniaux, A.M.D., Rival, X.: The ASTREÉ analyzer. In: Sagiv, M. (ed.) ESOP 2005. LNCS, vol. 3444, Springer, Heidelberg (2005)
Cuijpers, P., Reniers, M.: Hybrid process algebra. Journal of Logic and Algebraic Programming 62(2), 191–245 (2005)
Edalat, A., Lieutier, A.: Domain theory and differential calculus. Mathematical Structures in Computer Science 14(6), 771–802 (2002)
Edalat, A., Lieutier, A., Pattinson, D.: A computational model for multi-variable differential calculus. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, Springer, Heidelberg (2005)
Edalat, A., Pattinson, D.: Denotational Semantics of Hybrid Automata. In: Aceto, L., Ingólfsdóttir, A. (eds.) FOSSACS 2006 and ETAPS 2006. LNCS, vol. 3921, pp. 231–245. Springer, Heidelberg (2006)
Alur, R., et al.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138(1), 3–34 (1995)
Goubault, E., Martel, M., Putot, S.: Asserting the precision of floating-point computations: A simple abstract interpreter. In: Le Métayer, D. (ed.) ESOP 2002. LNCS, vol. 2305, pp. 209–212. Springer, Heidelberg (2002)
Goubault, E., Martel, M., Putot, S.: Some future challenges in the validation of control systems. In: ERTS (2006)
Gupta, V., Jagadeesan, R., Saraswat, V.: Computing with continuous change. Science of Computer Programming 30(1–2), 3–49 (1998)
Henzinger, T.A.: The theory of hybrid automata. In: Symposium on Logic in Computer Science, pp. 278–292. IEEE Computer Society Press, Los Alamitos (1996)
Henzinger, T.A., Ho, P.H., Wong-Toi, H.: Algorithmic analysis of nonlinear hybrid systems. IEEE Transactions on Automatic Control 43, 540–554 (1998)
Kowalewski, S., Stursberg, O., Fritz, M., Graf, H., Preuß, I.H.J.: A case study in tool-aided analysis of discretely controlled continuous systems: the two tanks problem. In: Antsaklis, P.J., Kohn, W., Lemmon, M.D., Nerode, A., Sastry, S.S. (eds.) HS 1997. LNCS, vol. 1567, Springer, Heidelberg (1999)
Martin, K.: A Foundation for Computation. PhD thesis, Department of Mathematics, Tulane University (2000)
Mycroft, A.: Abstract interpretation and Optimizing Transformations for Applicative Programs. PhD thesis, University of Edinburgh (1981)
Nedialkov, N.S., Jackson, K.R., Corliss, G.F.: Validated solutions of initial value problems for ordinary differential equations. Applied Mathematics and Computation 105(1), 21–68 (1999)
Tarski, A.: A lattice-theoretical fixpoint theorem and its applications. Pacific Journal of Mathematics 5, 285–309 (1955)
van Beek, D., Man, K., Reniers, M., Rooda, J., Schiffelers, R.: Syntax and consistent equation semantics of hybrid chi. Journal of Logic and Algebraic Programming 68(1-2), 129–210 (2006)
Winskel, G.: The formal semantics of programming languages: an introduction. MIT Press, Cambridge (1993)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Bouissou, O., Martel, M. (2008). A Hybrid Denotational Semantics for Hybrid Systems. In: Drossopoulou, S. (eds) Programming Languages and Systems. ESOP 2008. Lecture Notes in Computer Science, vol 4960. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-78739-6_5
Download citation
DOI: https://doi.org/10.1007/978-3-540-78739-6_5
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-78738-9
Online ISBN: 978-3-540-78739-6
eBook Packages: Computer ScienceComputer Science (R0)