Abstract
Timed automata due to Rajeev Alur and David Dill are the primary model for verifying properties of real-time systems with a continuous time domain. UPPAAL developed by Kim G. Larsen and Wang Yi and their collaborators is the main tool for practically performing such verifications. However, timed automata are in general not implementable. An automata model that enables implementation on the platform of Programmable Logic Controllers are PLC-Automata introduced by Henning Dierks. By translating them into timed automata, properties of PLC-Automata can be verified. We show this for properties formulated by counterexample formulas. The presentation is based on our book “Real-Time Systems” with Henning Dierks.
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References
Alur, R., Courcoubetis, C., Dill, D.L.: Model-checking in dense real-time. Inf. Comput. 104, 2–34 (1993). https://doi.org/10.1006/INCO.1993.1024
Alur, R., Dill, D.L.: A theory of timed automata. Theor. Comput. Sci. 126, 183–235 (1994). https://doi.org/10.1016/0304-3975(94)90010-8
Bengtsson, J., Yi, W.: Timed automata: semantics, algorithms and tools. In: Desel, J., Reisig, W., Rozenberg, G. (eds.) Lectures on Concurrency and Petri Nets, Advances in Petri Nets. LNCS, vol. 3098, pp. 87–124. Springer, Cham (2003). https://doi.org/10.1007/978-3-540-27755-2_3
Cassez, F., Henzinger, T.A., Raskin, J.: A comparison of control problems for timed and hybrid systems. In: Tomlin, C.J., Greenstreet, M.R. (eds.) Hybrid Systems: Computation and Control, 5th International Workshop, HSCC 2002, Proceedings. LNCS, vol. 2289, pp. 134–148. Springer (2002). https://doi.org/10.1007/3-540-45873-5
Dierks, H.: PLC-automata: a new class of implementable real-time automata. Theor. Comp. Sci. 253, 61–93 (2001). https://doi.org/10.1016/S0304-3975(00)00089-X
Dierks, H.: Time, Abstraction and Heuristics – Automatic Verification and Planning of Timed Systems using Abstraction and Heuristics, Berichte aus dem Department für Informatik, vol. 01-06. Universität Oldenburg (2006), Habilitationsschrift
Dierks, H., Fehnker, A., Mader, A., Vaandrager, F.W.: Operational and logical semantics for polling real-time systems. In: Ravn, A.P., Rischel, H. (eds.) Formal Techniques in Real-Time and Fault-Tolerant Systems, 5th International Symposium, FTRTFT’98, Proceedings. LNCS, vol. 1486, pp. 29–40. Springer (1998). https://doi.org/10.1007/BFB0055334
Dierks, H., Kupferschmid, S., Larsen, K.G.: Automatic abstraction refinement for timed automata. In: Raskin, J., Thiagarajan, P.S. (eds.) Formal Modeling and Analysis of Timed Systems, 5th International Conference, FORMATS 2007, Proceedings. LNCS, vol. 4763, pp. 114–129. Springer (2007). https://doi.org/10.1007/978-3-540-75454-1
Feo-Arenis, S., Vujinovic, M., Westphal, B.: On implementable timed automata. In: Gotsman, A., Sokolova, A. (eds.) Formal Techniques for Distributed Objects, Components, and Systems, FORTE 2020, Proceedings. LNCS, vol. 12136, pp. 78–95. Springer (2020). https://doi.org/10.1007/978-3-030-50086-3
Henzinger, T., Nicollin, X., Sifakis, J., Yovine, S.: Symbolic model checking for real-time systems. Inf. Comput. 111, 193–244 (1994). https://doi.org/10.1006/INCO.1994.1045
Hoenicke, J.: Combination of processes, data, and time. Ph.D. Thesis, Report Nr. 9/2006, University of Oldenburg (2006), https://d-nb.info/981576087
IEC International Standard 1131-3, Programmable Controllers, Part 3, Programming Languages (1993)
Kiviriga, A., Larsen, K.G., Nyman, U.: Randomized reachability analysis in UPPAAL: fast error detection in timed systems. Int. J. Softw. Tools Technol. Trans. 24(6), 1025–1042 (2022). https://doi.org/10.1007/S10009-022-00681-Z
Koymans, R.: Specifying real-time properties with metric temporal logic. Real-Time Syst. 2, 255–299 (1990). https://doi.org/10.1007/BF01995674
Krieg-Brückner, B., Peleska, J., Olderog, E.R., Baer, A.: The UniForM workbench, a universal development environment for formal methods. In: Wing, J.M., Woodcock, J., Davies, J. (eds.) FM’99 – Formal Methods, World Congress on Formal Methods in the Development of Computing Systems, Proceedings, Vol. II. LNCS, vol. 1709, pp. 1186–1205. Springer (1999).https://doi.org/10.1007/3-540-48118-4
Larsen, K.G., Petterson, P., Yi, W.: Uppaal in a nutshell. STTT Int. J. Softw. Tools Technol. Trans. 1, 134–152 (1997). https://doi.org/10.1007/S100090050010
Lewis, R.W.: Programming industrial control systems using IEC 1131-3. The Institution of Electrical Engineers (1998). https://doi.org/10.1049/PBCE050E, Revised Edition
Milner, R.: Communication and Concurrency. Prentice-Hall International, Hoboken (1989)
Olderog, E.R., Dierks, H.: Real-Time Systems - Formal Specification and Automatic Verification. Cambridge University Press, Cambridge (2008). https://doi.org/10.1017/CBO9780511619953
Olderog, E.R., Swaminathan, M.: Structural transformations for data-enriched real-time systems. Formal Aspects Comput. 27(4), 727–750 (2015). https://doi.org/10.1007/S00165-014-0306-Y
Ravn, A.P.: Design of embedded real-time computing systems. Tech. Rep. ID-TR 1995-170, Technical University of Denmark (October 1995), Thesis of the degree of Doctor Technics, ISSN 0902-2821
Wulf, M.D., Doyen, L., Raskin, J.F.: Almost ASAP semantics: from timed models to timed implementations. Formal Aspects Comput. 17, 319–341 (2005). https://doi.org/10.1007/S00165-005-0067-8
Zhou, C., Hansen, M.R.: Duration calculus: a formal approach to real-time systems. In: Monographs in Theoretical Computer Science. An EATCS Series, Springer (2004). https://doi.org/10.1007/978-3-662-06784-0
Zhou, C., Hansen, M.R., Sestoft, P.: Decidability and undecidability results for duration calculus. In: Enjalbert, P., Finkel, A., Wagner, K. (eds.) Symposium on Theoretical Aspects of Computer Science (STACS 93). LNCS, vol. 665, pp. 58–68. Springer, Cham (1993). https://doi.org/10.1007/3-540-56503-5
Zhou, C., Hoare, C.A.R., Ravn, A.P.: A calculus of durations. Inf. Process. Lett. 40, 269–276 (1991). https://doi.org/10.1016/0020-0190(91)90122-X
Acknowledgement
The author thanks Christopher Bischopink for suggesting the example in Sect. 3.
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Olderog, ER. (2025). Verifying PLC-Automata Against Counterexample Formulas Using Timed Automata. In: Graf, S., Pettersson, P., Steffen, B. (eds) Real Time and Such. Lecture Notes in Computer Science, vol 15230. Springer, Cham. https://doi.org/10.1007/978-3-031-73751-0_5
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