Abstract
The extension of timed formalisms to a hybrid setting with urgency, has been carried out in a rather straightforward manner, seemingly without difficulty. However, in this paper, we show that the combination of urgency with abstraction from continuous variables leads to undesired behavior. Abstraction from continuous variables ultimately leads to a timed system again, but with a much richer set of possible branching behaviors than a timed system that comprises only clocks. As it turns out, the formal definition of urgency, as defined for timed systems with clocks, does not fit our intuition of urgency anymore when applied to a timed system that is an abstraction of a hybrid system. Therefore, we propose to extend the formal semantics of timed and hybrid systems with guard trajectories. In this way, the continuous branching behavior introduced by hybrid systems remains visible even after abstraction from continuous variables. The practical applicability of the introduction of guard trajectories is illustrated by our revision of the structured operational semantics of the CIF language. The interplay between urgency and abstraction now adheres to our intuition, while compositionality with respect to urgency, variable abstraction, and parallel composition, is retained. In the future, symbolic elimination of urgency can be used to ensure that guard trajectories do not need to be actually calculated.
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References
Alur, R., Dill, D.: A theory of timed automata. Theoretical Computer Science 126, 183–235 (1994)
Larsen, K., Pettersson, P., Yi, W.: UPPAAL in a nutshell. International Journal on Software Tools for Technology Transfer 1(1-2), 134–152 (1997)
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)
Bozga, M., Mounier, L., Graf, S.: If-2.0: A validation environment for component-based real-time systems. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 343–348. Springer, Heidelberg (2002)
Henzinger, T.: The theory of hybrid automata. In: Verification of Digital and Hybrid Systems. NATO ASI Series F: Computer and Systems Science, vol. 170, pp. 265–292. Springer, Heidelberg (2000)
Lynch, N., Segala, R., Vaandrager, F.: Hybrid I/O automata revisited. In: Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.) HSCC 2001. LNCS, vol. 2034, pp. 403–417. Springer, Heidelberg (2001)
Henzinger, T., Ho, P.H., Wong-toi, H.: HyTech: A model checker for hybrid systems. International Journal on Software Tools for Technology Transfer 1(1), 110–122 (1997)
Lee, E., Zheng, H.: Operational semantics of hybrid systems. In: Morari, M., Thiele, L. (eds.) HSCC 2005. LNCS, vol. 3414, pp. 25–53. Springer, Heidelberg (2005)
Reynolds, J.C.: Theories of programming languages. Cambridge University Press, New York (1999)
Beek, D.A.v., Man, K.L., Reniers, M.A., Rooda, J.E., Schiffelers, R.R.H.: Syntax and consistent equation semantics of hybrid Chi. Journal of Logic and Algebraic Programming 68(1-2), 129–210 (2006)
Plotkin, G.: A structural approach to operational semantics. Technical Report DAIMI FN-19, Computer Science Department, Aarhus University (1981)
Beek, D.A.v., Collins, P., Nadales, D.E., Rooda, J., Schiffelers, R.R.H.: New concepts in the abstract format of the compositional interchange format. In: ADHS 2009, pp. 250–255. IFAC (2009)
Systems Engineering Institute: The Compositional Interchange Format for Hybrid Systems (2010), http://se.wtb.tue.nl/sewiki/cif/start
Cuijpers, P., Reniers, M.: Lost in translation: Hybrid-time flows vs real-time transitions. In: Egerstedt, M., Mishra, B. (eds.) HSCC 2008. LNCS, vol. 4981, pp. 116–129. Springer, Heidelberg (2008)
Alur, R., Henzinger, T.: Real-time system = discrete system + clock variables. In: Theories and Experiences for Real-time System Development. AMAST Series in Computing, vol. 2, pp. 1–29. World Scientific, Singapore (1993)
Kaynar, D., Lynch, N., Segala, R., Vaandrager, F.: A framework for modelling timed systems with restricted hybrid automata. In: RTSS 2003, pp. 166–178. IEEE Computer Society Press, Los Alamitos (2003)
Bornot, S., Sifakis, J., Tripakis, S.: Modeling urgency in timed systems. In: de Roever, W.-P., Langmaack, H., Pnueli, A. (eds.) COMPOS 1997. LNCS, vol. 1536, pp. 103–129. Springer, Heidelberg (1998)
Sifakis, J.: The compositional specification of timed systems. In: Halbwachs, N., Peled, D.A. (eds.) CAV 1999. LNCS, vol. 1633, pp. 2–7. Springer, Heidelberg (1999)
Bornot, S., Sifakis, J.: An algebraic framework for urgency. Information and Computation 163, 172–202 (2000)
D’Argenio, P., Gebremichael, B.: The coarsest congruence for timed automata with deadlines contained in bisimulation. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 125–140. Springer, Heidelberg (2005)
Bowman, H.: Modeling timeouts without timelocks. In: Katoen, J.-P. (ed.) AMAST-ARTS 1999, ARTS 1999, and AMAST-WS 1999. LNCS, vol. 1601, pp. 20–35. Springer, Heidelberg (1999)
Bohnenkamp, H., D’Argenio, P., Hermanns, H., Katoen, J.P.: MODEST: A compositional modeling formalism for hard and softly timed systems. IEEE Transactions on Software Engineering 32(10), 812–830 (2006)
Gebremichael, B., Vaandrager, F.: Specifying urgency in timed I/O automata. In: SEFM 2005, pp. 64–74. IEEE Computer Society, Los Alamitos (2005)
Mufti, W., Tcherukine, D.: Integration of model-checking tools: from discrete to hybrid models. In: INMIC 2007, pp. 1–4. IEEE International, Los Alamitos (2007)
Bornot, S., Sifakis, J.: On the composition of hybrid systems. In: Henzinger, T.A., Sastry, S.S. (eds.) HSCC 1998. LNCS, vol. 1386, pp. 49–63. Springer, Heidelberg (1998)
van Beek, D., Hofkamp, A., Reniers, M., Rooda, J., Schiffelers, R.: Syntax and formal semantics of Chi 2.0. SE Report 2008-01, Eindhoven University of Technology (2008)
Cuijpers, P., Reniers, M., Heemels, W.: Hybrid transition systems. Technical Report CS-Report 02-12, TU/e, Eindhoven, Netherlands (2002)
van Beek, D.A., Reniers, M.A., Schiffelers, R.R.H., Rooda, J.E.: Foundations of a compositional interchange format for hybrid systems. In: Bemporad, A., Bicchi, A., Buttazzo, G. (eds.) HSCC 2007. LNCS, vol. 4416, pp. 587–600. Springer, Heidelberg (2007)
Scott, D.: Outline of a mathematical theory of computation. In: CISS 1970, Princeton, pp. 169–176 (1970)
Mousavi, M.R., Reniers, M.A., Groote, J.F.: Notions of bisimulation and congruence formats for SOS with data. Information and Computation 200(1), 107–147 (2005)
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van Beek, D.A., Cuijpers, P.J.L., Markovski, J., Nadales Agut, D.E., Rooda, J.E. (2010). Reconciling Urgency and Variable Abstraction in a Hybrid Compositional Setting. In: Chatterjee, K., Henzinger, T.A. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2010. Lecture Notes in Computer Science, vol 6246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15297-9_6
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