Abstract
This article aims at providing a concise and precise Travellers Guide, Phrase Book or Reference Manual to the timed automata modeling formalism introduced by Alur and Dill [8, 9]. The paper gives comprehensive definitions of timed automata, priced (or weighted) timed automata, timed games, stochastic timed automata and highlights a number of results on associated decision problems related to model checking, equivalence checking, optimal scheduling, the existence of winning strategies, and then statistical model checking.
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References
Abdeddaïm, Y., Kerbaa, A., Maler, O.: Task graph scheduling using timed automata. In: IPDPS, p. 237. IEEE Computer Society (2003)
Aceto, L., Ingólfsdóttir, A., Larsen, K.G., Srba, J.: Reactive Systems: Modeling, Specification and Verification. Cambridge University Press (2007)
Allamigeon, X., Gaubert, S., Goubault, É.: Inferring min and max invariants using max-plus polyhedra. In: Alpuente, M., Vidal, G. (eds.) SAS 2008. LNCS, vol. 5079, pp. 189–204. Springer, Heidelberg (2008)
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)
Alur, R.: Timed automata. In: Halbwachs, Peled (eds.) [66], pp. 8–22
Alur, R., Bernadsky, M., Madhusudan, P.: Optimal reachability for weighted timed games. In: Díaz, J., Karhumäki, J., Lepistö, A., Sannella, D. (eds.) ICALP 2004. LNCS, vol. 3142, pp. 122–133. Springer, Heidelberg (2004)
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking for real-time systems. In: LICS, pp. 414–425. IEEE Computer Society (1990)
Alur, R., Dill, D.L.: Automata for modeling real-time systems. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 322–335. Springer, Heidelberg (1990)
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126(2), 183–235 (1994)
Alur, R., La Torre, S., Pappas, G.J.: Optimal paths in weighted timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [26], pp. 49–62
Andersson, D.: Improved combinatorial algorithms for discounted payoff games. Master’s thesis, Uppsala University, Department of Information Technology (2006)
Asarin, E., Bozga, M., Kerbrat, A., Maler, O., Pnueli, A., Rasse, A.: Data-structures for the verification of timed automata. In: Maler, O. (ed.) HART 1997. LNCS, vol. 1201, pp. 346–360. Springer, Heidelberg (1997)
Asarin, E., Maler, O., Pnueli, A.: Symbolic controller synthesis for discrete and timed systems. In: Antsaklis, P.J., Kohn, W., Nerode, A., Sastry, S. (eds.) HS 1994. LNCS, vol. 999, pp. 1–20. Springer, Heidelberg (1995)
Baier, C., Bertrand, N., Bouyer, P., Brihaye, T., Größer, M.: Probabilistic and topological semantics for timed automata. In: Arvind, V., Prasad, S. (eds.) FSTTCS 2007. LNCS, vol. 4855, pp. 179–191. Springer, Heidelberg (2007)
Barbot, B., Chen, T., Han, T., Katoen, J.-P., Mereacre, A.: Efficient CTMC model checking of linear real-time objectives. In: Abdulla, P.A., Leino, K.R.M. (eds.) TACAS 2011. LNCS, vol. 6605, pp. 128–142. Springer, Heidelberg (2011)
Behrmann, G., Bengtsson, J., David, A., Larsen, K.G., Pettersson, P., Yi, W.: Uppaal implementation secrets. In: Damm, W., Olderog, E.-R. (eds.) FTRTFT 2002. LNCS, vol. 2469, pp. 3–22. Springer, Heidelberg (2002)
Behrmann, G., Bouyer, P., Larsen, K.G., Pelánek, R.: Lower and upper bounds in zone based abstractions of timed automata. In: Jensen, Podelski (eds.) [74], pp. 312–326
Behrmann, G., Brinksma, E., Hendriks, M., Mader, A.: Production scheduling by reachability analysis - a case study. In: IPDPS. IEEE Computer Society (2005)
Behrmann, G., Cougnard, A., David, A., Fleury, E., Larsen, K.G., Lime, D.: Uppaal-Tiga: Time for playing games! In: Damm, W., Hermanns, H. (eds.) CAV 2007. LNCS, vol. 4590, pp. 121–125. Springer, Heidelberg (2007)
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)
Behrmann, G., Fehnker, A., Hune, T., Larsen, K.G., Pettersson, P., Romijn, J., Vaandrager, F.W.: Minimum-cost reachability for priced timed automata. In: Benedetto, Sangiovanni-Vincentelli (eds.) [26], pp. 147–161
Behrmann, G., Hune, T., Vaandrager, F.W.: Distributing timed model checking - how the search order matters. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 216–231. Springer, Heidelberg (2000)
Behrmann, G., Larsen, K.G., Pearson, J., Weise, C., Yi, W.: Efficient timed reachability analysis using clock difference diagrams. In: Halbwachs, Peled (eds.) [66], pp. 341–353
Behrmann, G., Larsen, K.G., Pelánek, R.: To store or not to store. In: Hunt Jr., W.A., Somenzi, F. (eds.) CAV 2003. LNCS, vol. 2725, pp. 433–445. Springer, Heidelberg (2003)
Behrmann, G., Larsen, K.G., Rasmussen, J.I.: Optimal scheduling using priced timed automata. SIGMETRICS Performance Evaluation Review 32(4), 34–40 (2005)
Di Benedetto, M.D., Sangiovanni-Vincentelli, A.L. (eds.): HSCC 2001. LNCS, vol. 2034. Springer, Heidelberg (2001)
Bengtsson, J.E., Yi, W.: On clock difference constraints and termination in reachability analysis of timed automata. In: Dong, J.S., Woodcock, J. (eds.) ICFEM 2003. LNCS, vol. 2885, pp. 491–503. Springer, Heidelberg (2003)
Bengtsson, J.E., Yi, W.: Timed automata: Semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) ACPN 2003,. LNCS, vol. 3098, pp. 87–124. Springer, Heidelberg (2004)
Bérard, B., Petit, A., Diekert, V., Gastin, P.: Characterization of the expressive power of silent transitions in timed automata. Fundam. Inform. 36(2-3), 145–182 (1998)
Bertrand, N., Bouyer, P., Brihaye, T., Markey, N.: Quantitative model-checking of one-clock timed automata under probabilistic semantics. In: QEST, pp. 55–64. IEEE Computer Society (2008)
Bohnenkamp, H., D’Argenio, P.R., Hermanns, H., Katoen, J.-P.: Modest: A compositional modeling formalism for real-time and stochastic systems. Technical Report CTIT 04-46, University of Twente (2004)
Bouyer, P.: Untameable timed automata! In: Alt, H., Habib, M. (eds.) STACS 2003. LNCS, vol. 2607, pp. 620–631. Springer, Heidelberg (2003)
Bouyer, P., Brihaye, T., Markey, N.: Improved undecidability results on weighted timed automata. Inf. Process. Lett. 98(5), 188–194 (2006)
Bouyer, P., Brinksma, E., Larsen, K.G.: Staying alive as cheaply as possible. In: Alur, R., Pappas, G.J. (eds.) HSCC 2004. LNCS, vol. 2993, pp. 203–218. Springer, Heidelberg (2004)
Bouyer, P., Cassez, F., Fleury, E., Larsen, K.G.: Optimal strategies in priced timed game automata. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS 2004. LNCS, vol. 3328, pp. 148–160. Springer, Heidelberg (2004)
Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N.: Timed automata with observers under energy constraints. In: HSCC, pp. 61–70. ACM (2010)
Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Srba, J.: Infinite runs in weighted timed automata with energy constraints. In: Cassez, F., Jard, C. (eds.) FORMATS 2008. LNCS, vol. 5215, pp. 33–47. Springer, Heidelberg (2008)
Bouyer, P., Larsen, K.G., Markey, N.: Lower-bound constrained runs in weighted timed automata. In: QEST, pp. 128–137. IEEE Computer Society (2012)
Bouyer, P., Larsen, K.G., Markey, N., Rasmussen, J.I.: Almost optimal strategies in one clock priced timed games. In: Arun-Kumar, S., Garg, N. (eds.) FSTTCS 2006. LNCS, vol. 4337, pp. 345–356. Springer, Heidelberg (2006)
Bozga, M., Daws, C., Maler, O., Olivero, A., Tripakis, S., Yovine, S.: Kronos: A model-checking tool for real-time systems. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 546–550. Springer, Heidelberg (1998)
Brihaye, T., Bruyère, V., Raskin, J.-F.: On optimal timed strategies. In: Pettersson, Yi (eds.) [96], pp. 49–64
Bulychev, P., David, A., Larsen, K.G., Legay, A., Li, G., Bøgsted Poulsen, D., Stainer, A.: Monitor-based statistical model checking for weighted metric temporal logic. In: Bjørner, N., Voronkov, A. (eds.) LPAR-18 2012. LNCS, vol. 7180, pp. 168–182. Springer, Heidelberg (2012)
Bulychev, P.E., David, A., Larsen, K.G., Legay, A., Mikučionis, M.: Computing Nash equilibrium in wireless ad hoc networks: A simulation-based approach. In: Reich, J., Finkbeiner, B. (eds.) IWIGP. EPTCS, vol. 78, pp. 1–14 (2012)
Cassez, F., David, A., Fleury, E., Larsen, K.G., Lime, D.: Efficient on-the-fly algorithms for the analysis of timed games. In: Abadi, M., de Alfaro, L. (eds.) CONCUR 2005. LNCS, vol. 3653, pp. 66–80. Springer, Heidelberg (2005)
Cassez, F., David, A., Larsen, K.G., Lime, D., Raskin, J.-F.: Timed control with observation based and stuttering invariant strategies. In: Namjoshi, K.S., Yoneda, T., Higashino, T., Okamura, Y. (eds.) ATVA 2007. LNCS, vol. 4762, pp. 192–206. Springer, Heidelberg (2007)
Čerāns, K.: Decidability of bisimulation equivalences for parallel timer processes. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 302–315. Springer, Heidelberg (1993)
Chatterjee, K., Doyen, L.: Energy parity games. In: Abramsky, S., Gavoille, C., Kirchner, C., Meyer auf der Heide, F., Spirakis, P.G. (eds.) ICALP 2010. LNCS, vol. 6199, pp. 599–610. Springer, Heidelberg (2010)
Chatterjee, K., Doyen, L., Henzinger, T.A., Raskin, J.-F.: Generalized mean-payoff and energy games. In: Lodaya, K., Mahajan, M. (eds.) FSTTCS. LIPIcs, vol. 8, pp. 505–516 (2010)
Courcoubetis, C., Yannakakis, M.: Minimum and maximum delay problems in real-time systems. In: Larsen, Skou (eds.) [86], pp. 399–409
D’Argenio, P.R., Katoen, J.-P., Ruys, T.C., Tretmans, J.: The bounded retransmission protocol must be on time! In: Brinksma, E. (ed.) TACAS 1997. LNCS, vol. 1217, pp. 416–431. Springer, Heidelberg (1997)
David, A., Du, D., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Statistical model checking for stochastic hybrid systems. In: HSB. EPTCS, vol. 92, pp. 122–136 (2012)
David, A., Larsen, K.G., Legay, A., Mikucionis, M., Poulsen, D.B., Sedwards, S.: Runtime verification of biological systems. In: Margaria, T., Steffen, B. (eds.) ISoLA 2012, Part I. LNCS, vol. 7609, pp. 388–404. Springer, Heidelberg (2012)
David, A., Larsen, K.G., Legay, A., Mikučionis, M., Poulsen, D.B., van Vliet, J., Wang, Z.: Statistical model checking for networks of priced timed automata. In: Fahrenberg, U., Tripakis, S. (eds.) FORMATS 2011. LNCS, vol. 6919, pp. 80–96. Springer, Heidelberg (2011)
David, A., Larsen, K.G., Legay, A., Mikučionis, M., Wang, Z.: Time for statistical model checking of real-time systems. In: Gopalakrishnan, G., Qadeer, S. (eds.) CAV 2011. LNCS, vol. 6806, pp. 349–355. Springer, Heidelberg (2011)
Dill, D.L.: Timing assumptions and verification of finite-state concurrent systems. In: Sifakis, J. (ed.) CAV 1989. LNCS, vol. 407, pp. 197–212. Springer, Heidelberg (1990)
Duflot, M., Kwiatkowska, M., Norman, G., Parker, D.: A formal analysis of bluetooth device discovery. International Journal on Software Tools for Technology Transfer (STTT) 8, 621–632 (2006)
Ernits, J.P.: Memory arbiter synthesis and verification for a radar memory interface card. Nord. J. Comput. 12(2), 68–88 (2005)
Fahrenberg, U., Juhl, L., Larsen, K.G., Srba, J.: Energy games in multiweighted automata. In: Cerone, A., Pihlajasaari, P. (eds.) ICTAC 2011. LNCS, vol. 6916, pp. 95–115. Springer, Heidelberg (2011)
Fahrenberg, U., Larsen, K.G.: Discount-optimal infinite runs in priced timed automata. Electr. Notes Theor. Comput. Sci. 239, 179–191 (2009)
Fahrenberg, U., Larsen, K.G.: Discounting in time. Electr. Notes Theor. Comput. Sci. 253(3), 25–31 (2009)
Fahrenberg, U., Larsen, K.G., Legay, A., Thrane, C.: Model-based verification, optimization, synthesis and performance evaluation of real-time systems. In: Proceedings of the NATO Advanced Study Institute on Engineering Methods and Tools for Software Safety and Security Marktoberdorf, Germany (August 2012) (to be published 2013)
Fahrenberg, U., Larsen, K.G., Thrane, C.: Verification, performance analysis and controller synthesis for real-time systems. In: Broy, M., Sitou, W., Hoare, T. (eds.) ASI 2008. NATO Science for Peace and Security Series - D: Information and Communication Security, vol. 22. IOS Press BV (2008)
Fahrenberg, U., Larsen, K.G., Thrane, C.R.: Verification, performance analysis and controller synthesis for real-time systems. In: Arbab, F., Sirjani, M. (eds.) FSEN 2009. LNCS, vol. 5961, pp. 34–61. Springer, Heidelberg (2010)
Fahrenberg, U., Larsen, K.G., Thrane, C.: Model-based verification and analysis for real-time systems. In: Broy, M., Leuxner, C., Hoare, T. (eds.) Software and Systems Safety - Specification and Verification. NATO Science for Peace and Security Series - D: Information and Communication Security, vol. 30, pp. 231–259. IOS Press (2011)
Fehnker, A.: Scheduling a steel plant with timed automata. In: RTCSA, pp. 280–286. IEEE Computer Society (1999)
Halbwachs, N., Peled, D. (eds.): CAV 1999. LNCS, vol. 1633. Springer, Heidelberg (1999)
Hansen, M.R., Madsen, J., Brekling, A.W.: Semantics and verification of a language for modelling hardware architectures. In: Jones, C.B., Liu, Z., Woodcock, J. (eds.) Formal Methods and Hybrid Real-Time Systems. LNCS, vol. 4700, pp. 300–319. Springer, Heidelberg (2007)
Hendriks, M.: Model checking the time to reach agreement. In: Pettersson, Yi (eds.) [96], pp. 98–111
Henzinger, T.A., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inf. Comput. 111(2), 193–244 (1994)
Hérault, T., Lassaigne, R., Magniette, F., Peyronnet, S.: Approximate probabilistic model checking. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 73–84. Springer, Heidelberg (2004)
Herbreteau, F., Kini, D., Srivathsan, B., Walukiewicz, I.: Using non-convex approximations for efficient analysis of timed automata. In: Chakraborty, S., Kumar, A. (eds.) FSTTCS. LIPIcs, vol. 13, pp. 78–89. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)
Hune, T., Larsen, K.G., Pettersson, P.: Guided synthesis of control programs using Uppaal. Nord. J. Comput. 8(1), 43–64 (2001)
Jensen, H.E., Guldstr, K., Skou, A.: Scaling up Uppaal. In: Joseph, M. (ed.) FTRTFT 2000. LNCS, vol. 1926, pp. 19–30. Springer, Heidelberg (2000)
Jensen, K., Podelski, A. (eds.): TACAS 2004. LNCS, vol. 2988. Springer, Heidelberg (2004)
Jessen, J.J., Rasmussen, J.I., Larsen, K.G., David, A.: Guided controller synthesis for climate controller using Uppaal Tiga. In: Raskin, J.-F., Thiagarajan, P.S. (eds.) FORMATS 2007. LNCS, vol. 4763, pp. 227–240. Springer, Heidelberg (2007)
Karp, R.M.: A characterization of the minimum cycle mean in a digraph. Disc. Math. 23(3), 309–311 (1978)
Kwiatkowska, M.Z., Norman, G., Parker, D.: PRISM 2.0: A tool for probabilistic model checking. In: QEST, pp. 322–323. IEEE (2004)
Lamport, L.: Real-time model checking is really simple. In: Borrione, D., Paul, W. (eds.) CHARME 2005. LNCS, vol. 3725, pp. 162–175. Springer, Heidelberg (2005)
Larsen, K.G., Behrmann, G., Brinksma, E., Fehnker, A., Hune, T., Pettersson, P., Romijn, J.M.T.: 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)
Larsen, K.G., Larsson, F., Pettersson, P., Yi, W.: Efficient verification of real-time systems: compact data structure and state-space reduction. In: IEEE Real-Time Systems Symposium, pp. 14–24. IEEE Computer Society (1997)
Larsen, K.G., Mikucionis, M., Nielsen, B., Skou, A.: Testing real-time embedded software using Uppaal-TRON: an industrial case study. In: Wolf, W. (ed.) EMSOFT, pp. 299–306. ACM (2005)
Larsen, K.G., Pearson, J., Weise, C., Yi, W.: Clock difference diagrams. Nord. J. Comput. 6(3), 271–298 (1999)
Larsen, K.G., Pettersson, P., Yi, W.: Uppaal in a nutshell. STTT 1(1-2), 134–152 (1997)
Larsen, K.G., Rasmussen, J.I.: Optimal conditional reachability for multi-priced timed automata. In: Sassone, V. (ed.) FOSSACS 2005. LNCS, vol. 3441, pp. 234–249. Springer, Heidelberg (2005)
Larsen, K.G., Rasmussen, J.I.: Optimal reachability for multi-priced timed automata. Theor. Comput. Sci. 390(2-3), 197–213 (2008)
Larsen, K.G., Skou, A. (eds.): CAV 1991. LNCS, vol. 575. Springer, Heidelberg (1992)
Lindahl, M., Pettersson, P., Yi, W.: Formal design and analysis of a gear controller. In: Steffen, B. (ed.) TACAS 1998. LNCS, vol. 1384, pp. 281–297. Springer, Heidelberg (1998)
Lu, Q., Madsen, M., Milata, M., Ravn, S., Fahrenberg, U., Larsen, K.G.: Reachability analysis for timed automata using max-plus algebra. J. Log. Algebr. Program. 81(3), 298–313 (2012)
Maler, O.: Timed automata as an underlying model for planning and scheduling. In: Fox, M., Coddington, A.M. (eds.) AIPS Workshop on Planning for Temporal Domains, pp. 67–70 (2002)
Maler, O., Larsen, K.G., Krogh, B.H.: On zone-based analysis of duration probabilistic automata. In: INFINITY. EPTCS, vol. 39, pp. 33–46 (2010)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems (an extended abstract). In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, Springer, Heidelberg (1995)
McDermott-Wells, P.: What is bluetooth? IEEE Potentials 23(5), 33–35 (2005)
Møller, J.B., Lichtenberg, J., Andersen, H.R., Hulgaard, H.: Difference decision diagrams. In: Flum, J., Rodríguez-Artalejo, M. (eds.) CSL 1999. LNCS, vol. 1683, pp. 111–125. Springer, Heidelberg (1999)
Ouaknine, J., Worrell, J.: Universality and language inclusion for open and closed timed automata. In: Maler, O., Pnueli, A. (eds.) HSCC 2003. LNCS, vol. 2623, pp. 375–388. Springer, Heidelberg (2003)
Panangaden, P.: Labelled Markov Processes. Imperial College Press (2010)
Pettersson, P., Yi, W. (eds.): FORMATS 2005. LNCS, vol. 3829. Springer, Heidelberg (2005)
Quaas, K.: On the interval-bound problem for weighted timed automata. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 452–464. Springer, Heidelberg (2011)
Rasmussen, J.I., Larsen, K.G., Subramani, K.: Resource-optimal scheduling using priced timed automata. In: Jensen, Podelski (eds.) [74], pp. 220–235.
Sen, K., Viswanathan, M., Agha, G.: Statistical model checking of black-box probabilistic systems. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 202–215. Springer, Heidelberg (2004)
Stirling, C.: Modal and temporal logics for processes. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 149–237. Springer, Heidelberg (1996)
Teige, T., Eggers, A., Fränzle, M.: Constraint-based analysis of concurrent probabilistic hybrid systems: An application to networked automation systems. Nonlinear Analysis: Hybrid Systems (2011)
Tripakis, S., Altisen, K.: On-the-fly controller synthesis for discrete and dense-time systems. In: Wing, J.M., Woodcock, J. (eds.) FM 1999. LNCS, vol. 1708, pp. 233–252. Springer, Heidelberg (1999)
van Hoesel, L.F.W., Havinga, P.J.M.: A lightweight medium access protocol (LMAC) for wireless sensor networks: Reducing preamble transmissions and transceiver state switches. In: 1st International Workshop on Networked Sensing Systems (INSS 2004), Tokio, Japan, pp. 205–208. Society of Instrument and Control Engineers (SICE) (2004)
Wald, A.: Sequential Analysis. Dover Publications (2004)
Yi, W., Pettersson, P., Daniels, M.: Automatic verification of real-time communicating systems by constraint-solving. In: Hogrefe, D., Leue, S. (eds.) FORTE. IFIP Conference Proceedings, vol. 6, pp. 243–258. Chapman & Hall (1994)
Younes, H.L.S.: Verification and Planning for Stochastic Processes with Asynchronous Events. PhD thesis, Carnegie Mellon (2005)
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Fahrenberg, U., Larsen, K.G., Legay, A. (2013). Model-Based Verification, Optimization, Synthesis and Performance Evaluation of Real-Time Systems. In: Liu, Z., Woodcock, J., Zhu, H. (eds) Unifying Theories of Programming and Formal Engineering Methods. Lecture Notes in Computer Science, vol 8050. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39721-9_2
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