Abstract
Hybrid Automata describe dynamical systems where continuous behaviour interacts with discrete events. Resource Timed Automata (RTA), a subset of Hybrid Automata, adopt an additive composition scheme, in which discrete behaviour of components is executed concurrently, time is synchronized, and the evolution of continuous variables is arithmetically added up. Additive composition facilitates modelling and analysis of cumulative properties of continuous variables, such as conservation laws, typically manifested as the balancing of real-valued variables. In this paper, we present and exemplify an assume-guarantee framework aimed at additive compositional reasoning in the setting of hybrid systems. Crucially, we introduce a notion of refinement on so-called Resource Hybrid Automata (RHA), and show that it is a pre-congruence for additive composition. Furthermore - crucial for our assume-guarantee framework – we show that RHAs are closed under conjunction and admit a so-called quotient constructions (a dual operator to parallel composition). Finally, we demonstrate how the Statistical Model Checking (SMC) engine of the tool UPPAAL may be used to efficiently falsify refinements.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
de Alfaro, L., Henzinger, T.A.: Interface automata. In: Tjoa, A.M., Gruhn, V. (eds.) Proceedings of the 8th European Software Engineering Conference held jointly with 9th ACM SIGSOFT International Symposium on Foundations of Software Engineering 2001, Vienna, Austria, 10–14 September 2001, pp. 109–120. ACM (2001). https://doi.org/10.1145/503209.503226
Alur, R., Dill, D.L.: A theory of timed automata. Theoret. Comput. Sci. 126(2), 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8
Bacci, G., Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Reynier, P.-A.: Optimal and robust controller synthesis. In: Havelund, K., Peleska, J., Roscoe, B., de Vink, E. (eds.) FM 2018. LNCS, vol. 10951, pp. 203–221. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-95582-7_12
Bauer, S.S., et al.: Moving from specifications to contracts in component-based design. In: de Lara, J., Zisman, A. (eds.) FASE 2012. LNCS, vol. 7212, pp. 43–58. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-28872-2_3
Benveniste, A., et al.: Contracts for system design. Found. Trends Electron. Des. Autom. 12(2–3), 124–400 (2018). https://doi.org/10.1561/1000000053
Bergstra, J.A., Klop, J.W.: Algebra of communicating processes with abstraction. Theor. Comput. Sci. 37, 77–121 (1985). https://doi.org/10.1016/0304-3975(85)90088-X
Boudol, G., Larsen, K.G.: Graphical versus logical specifications. In: Arnold, A. (ed.) CAAP 1990. LNCS, vol. 431, pp. 57–71. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52590-4_40
Bouyer, P., Colange, M., Markey, N.: Symbolic optimal reachability in weighted timed automata. In: Chaudhuri, S., Farzan, A. (eds.) CAV 2016. LNCS, vol. 9779, pp. 513–530. Springer, Cham (2016). https://doi.org/10.1007/978-3-319-41528-4_28
Caillaud, B., Delahaye, B., Larsen, K.G., Legay, A., Pedersen, M.L., Wasowski, A.: Constraint Markov chains. Theor. Comput. Sci. 412(34), 4373–4404 (2011). https://doi.org/10.1016/j.tcs.2011.05.010
Čerāns, K., Godskesen, J.C., Larsen, K.G.: Timed modal specification—theory and tools. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 253–267. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-56922-7_21
Cuijpers, P.J.L., Reniers, M.A.: 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). https://doi.org/10.1007/978-3-540-78929-1_9
David, A., et al.: Compositional verification of real-time systems using Ecdar. Int. J. Softw. Tools Technol. Transf. 14(6), 703–720 (2012). https://doi.org/10.1007/s10009-012-0237-y
David, A., Larsen, K.G., Legay, A., Mikuăionis, M., Poulsen, D.B.: UPPAAL SMC tutorial. Int. J. Softw. Tools Technol. Transf. 17(4), 397–415 (2015). https://doi.org/10.1007/s10009-014-0361-y
David, A., Larsen, K.G., Legay, A., Nyman, U., Wasowski, A.: Timed I/O automata: a complete specification theory for real-time systems. In: Johansson, K.H., Yi, W. (eds.) Proceedings of the 13th ACM International Conference on Hybrid Systems: Computation and Control, HSCC 2010, Stockholm, Sweden, 12–15 April 2010, pp. 91–100. ACM (2010). https://doi.org/10.1145/1755952.1755967
van Glabbeek, R.J.: The linear time - branching time spectrum I: the semantics of concrete, sequential processes. In: Bergstra, J.A., Ponse, A., Smolka, S.A. (eds.) Handbook of Process Algebra, chap. 1, pp. 3–99. Elsevier Science, Amsterdam (2001). https://doi.org/10.1016/B978-044482830-9/50019-9
Hansen, J., Larsen, K.G., Cuijpers, P.J.L.: Balancing flexible production and consumption of energy using resource timed automata. In: 2022 11th Mediterranean Conference on Embedded Computing (MECO), pp. 1–6 (2022). https://doi.org/10.1109/MECO55406.2022.9797191
He, J.: Process simulation and refinement. Formal Aspects Comput. 1(3), 229–241 (1989). https://doi.org/10.1007/BF01887207
Jifeng, H.: Various simulations and refinements. In: de Bakker, J.W., de Roever, W.-P., Rozenberg, G. (eds.) REX 1989. LNCS, vol. 430, pp. 340–360. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52559-9_70
He, J.: Service refinement. In: 15th Asia-Pacific Software Engineering Conference (APSEC 2008), 3–5 December 2008, Beijing, China, p. 5. IEEE Computer Society (2008). https://doi.org/10.1109/APSEC.2008.78
He, J., Hoare, C.A.R.: Unifying theories of programming. In: Orlowska, E., Szalas, A. (eds.) Participants Copies for Relational Methods in Logic, Algebra and Computer Science, 4th International Seminar RelMiCS, Warsaw, Poland, 14–20 September 1998, pp. 97–99 (1998)
He, J., Liu, Z., Li, X.: Towards a refinement calculus for object systems. In: Proceedings of the 1st IEEE International Conference on Cognitive Informatics (ICCI 2002), 19–20 August 2002, Calgary, Canada, pp. 69–76. IEEE Computer Society (2002). https://doi.org/10.1109/COGINF.2002.1039284
Henzinger, T.A., Kurshan, R.P.: The theory of hybrid automata. In: Inan, M.K., Kurshan, R.P. (eds.) Verification of Digital and Hybrid Systems. NATO ASI Series, vol. 170, pp. 265–292. Springer, Heidelberg (2000)
Hoare, C.A.R.: Communicating Sequential Processes. International Series in Computer Science. Prentice Hall (1985)
Hoare, C.A.R., He, J.: The weakest prespecification. Inf. Process. Lett. 24(2), 127–132 (1987). https://doi.org/10.1016/0020-0190(87)90106-2
Hoare, T., He, J.: Unifying theories for parallel programming. In: Lengauer, C., Griebl, M., Gorlatch, S. (eds.) Euro-Par 1997. LNCS, vol. 1300, pp. 15–30. Springer, Heidelberg (1997). https://doi.org/10.1007/BFb0002714
Hoare, C.A.R., He, J., Sanders, J.W.: Prespecification in data refinement. Inf. Process. Lett. 25(2), 71–76 (1987). https://doi.org/10.1016/0020-0190(87)90224-9
Jones, C.B.: Developing methods for computer programs including a notion of interference. Ph.D. thesis, University of Oxford, UK (1981). https://ethos.bl.uk/OrderDetails.do?uin=uk.bl.ethos.259064
Lamport, L.: Hybrid systems in TLA\(^{+}\). In: Grossman, R.L., Nerode, A., Ravn, A.P., Rischel, H. (eds.) HS 1991-1992. LNCS, vol. 736, pp. 77–102. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57318-6_25
Larsen, K., et al.: As cheap as possible: efficient cost-optimal reachability for priced timed automata. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 493–505. Springer, Heidelberg (2001). https://doi.org/10.1007/3-540-44585-4_47
Larsen, K.G.: Modal specifications. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 232–246. Springer, Heidelberg (1990). https://doi.org/10.1007/3-540-52148-8_19
Larsen, K.G., Rasmussen, J.I.: Optimal reachability for multi-priced timed automata. Theor. Comput. Sci. 390(2), 197–213 (2008). https://doi.org/10.1016/j.tcs.2007.09.021. Foundations Software Science and Computational Structures
Larsen, K.G., Steffen, B., Weise, C.: The methodology of modal constraints. In: Broy, M., Merz, S., Spies, K. (eds.) Formal Systems Specification. LNCS, vol. 1169, pp. 405–435. Springer, Heidelberg (1996). https://doi.org/10.1007/BFb0024437
Larsen, K.G., Thomsen, B.: A modal process logic. In: Proceedings of the Third Annual Symposium on Logic in Computer Science (LICS 1988), Edinburgh, Scotland, UK, 5–8 July 1988, pp. 203–210. IEEE Computer Society (1988). https://doi.org/10.1109/LICS.1988.5119
Milner, R.: A Calculus of Communicating Systems. Lecture Notes in Computer Science, vol. 92. Springer, Cham (1980). https://doi.org/10.1007/3-540-10235-3
Owicki, S.S., Gries, D.: An axiomatic proof technique for parallel programs I. Acta Inform. 6, 319–340 (1976). https://doi.org/10.1007/BF00268134
Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57 (1977). https://doi.org/10.1109/SFCS.1977.32
Scholefield, D., Zedan, H., Jifeng, H.: Real-time refinement: semantics and application. In: Borzyszkowski, A.M., Sokołowski, S. (eds.) MFCS 1993. LNCS, vol. 711, pp. 693–702. Springer, Heidelberg (1993). https://doi.org/10.1007/3-540-57182-5_60
Xu, Q., de Roever, W.P., He, J.: The rely-guarantee method for verifying shared variable concurrent programs. Formal Aspects Comput. 9(2), 149–174 (1997). https://doi.org/10.1007/BF01211617
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2023 The Author(s), under exclusive license to Springer Nature Switzerland AG
About this chapter
Cite this chapter
Cuijpers, P.J.L., Hansen, J., Larsen, K.G. (2023). Assume-Guarantee Reasoning for Additive Hybrid Behaviour. In: Bowen, J.P., Li, Q., Xu, Q. (eds) Theories of Programming and Formal Methods. Lecture Notes in Computer Science, vol 14080. Springer, Cham. https://doi.org/10.1007/978-3-031-40436-8_11
Download citation
DOI: https://doi.org/10.1007/978-3-031-40436-8_11
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-031-40435-1
Online ISBN: 978-3-031-40436-8
eBook Packages: Computer ScienceComputer Science (R0)