Abstract
This paper is concerned with the refinement and control of a certain class of labelled transition systems, called plant automata, via bisimulation quotients. Refinement means that arbitrary transitions may be removed whereas control allows only removing edges with the same edge label. The goal is to ensure given LTL properties in the resulting plant automaton. We give a hardness result for refinement and control and investigate, in particular, the question whether refineability and controllability can be decided by looking at bisimulation quotients.
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Bacci, G., Bouyer, P., Fahrenberg, U., Larsen, K.G., Markey, N., Reynier, P.-A.: Optimal and robust controller synthesis using energy timed automata with uncertainty. Form. Asp. Comput. 33(1), 3–25 (2020). https://doi.org/10.1007/s00165-020-00521-4
Baier, C., Katoen, J.P.: Principles of Model Checking. MIT Press, Cambridge (2008)
Emerson, E.A., Jutla, C.S.: The complexity of tree automata and logics of programs. In: 29th Annual Symposium on Foundations of Computer Science, White Plains, New York, USA, 24–26 October 1988, pp. 328–337. IEEE Computer Society (1988)
Garey, M.R., Johnson, D.S.: Computers and Intractability: A Guide to the Theory of NP-Completeness. WH Freeman and Company, NY (1979)
Glück, R.: Bisimulations and model refinement (preprint). http://rolandglueck.de/html/PreprintDiss.pdf
Glück, R.: Using bisimulations for optimality problems in model refinement. In: de Swart, H. (ed.) RAMICS 2011. LNCS, vol. 6663, pp. 164–179. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-21070-9_14
Glück, R., Möller, B., Sintzoff, M.: A semiring approach to equivalences, bisimulations and control. In: Berghammer, R., Jaoua, A.M., Möller, B. (eds.) RelMiCS 2009. LNCS, vol. 5827, pp. 134–149. Springer, Heidelberg (2009). https://doi.org/10.1007/978-3-642-04639-1_10
Glück, R., Möller, B., Sintzoff, M.: Model refinement using bisimulation quotients. In: Johnson, M., Pavlovic, D. (eds.) AMAST 2010. LNCS, vol. 6486, pp. 76–91. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-17796-5_5
Glück, R.: Bisimulations and model refinement. PhD thesis, University of Augsburg. Pro Business (2015)
Maler, O., Pnueli, A., Sifakis, J.: On the synthesis of discrete controllers for timed systems. In: Mayr, E.W., Puech, C. (eds.) STACS 1995. LNCS, vol. 900, pp. 229–242. Springer, Heidelberg (1995). https://doi.org/10.1007/3-540-59042-0_76
Myhill, J.: Finite automata and the representation of events. WADD Tech. Rep. 57, 112–137 (1957)
Nerode, A.: Linear automaton transformations. Proc. Am. Math. Soc. 9(4), 541–544 (1958)
Paige, R., Tarjan, R.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)
Pous, D.: Complete lattices and up-to techniques. In: Shao, Z. (ed.) APLAS 2007. LNCS, vol. 4807, pp. 351–366. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-76637-7_24
Rabin, M.O.: Decidability of second-order theories and automata on infinite trees. Trans. Am. Math. Soc. 141, 1–35 (1969)
Ramadge, P.J., Wonham, W.M.: The control of discrete event systems. Proc. IEEE 77, 81–98 (1989)
Rey de Souza, F.G., Hirata, C.M., Nadjm-Tehrani, S.: Synthesis of a controller algorithm for safety-critical systems. IEEE Access 10, 76351–76375 (2022)
Schmidt, G., Ströhlein, T.: Relations and Graphs: Discrete Mathematics for Computer Scientists. Springer, Heidelberg (1993). https://doi.org/10.1007/978-3-642-77968-8
Sintzoff, M.: Synthesis of optimal control policies for some infinite-state transition systems. In: Audebaud, P., Paulin-Mohring, C. (eds.) MPC 2008. LNCS, vol. 5133, pp. 336–359. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-70594-9_18
Tarjan, R.: Depth-first search and linear graph algorithms. In: 12th Annual Symposium on Switching and Automata Theory (SWAT 1971), pp. 114–121 (1971)
Thistle, J.G., Wonham, W.M.: Control of \(\omega \)-automata, Church’s problem, and the emptiness problem for tree \(\omega \)-automata. In: Börger, E., Jäger, G., Kleine Büning, H., Richter, M.M. (eds.) CSL 1991. LNCS, vol. 626, pp. 367–381. Springer, Heidelberg (1992). https://doi.org/10.1007/BFb0023782
Thistle, J.G., Wonham, W.M.: Control of infinite behavior of finite automata. SIAM J. Control Optim. 32(4), 1075–1097 (1994)
Bochmann, G.V., Hilscher, M., Linker, S., Olderog, E.-R.: Synthesizing and verifying controllers for multi-lane traffic maneuvers. Form. Asp. Comput. 29(4), 583–600 (2017). https://doi.org/10.1007/s00165-017-0424-4
Winter, M.: A relation-algebraic theory of bisimulations. Fundam. Inform. 83(4), 429–449 (2008)
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The author is grateful to Bernhard Möller and the anonymous reviewers for valuable hints and remarks which helped to improve quality and readability of the paper.
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Glück, R. (2023). Compatibility of Refining and Controlling Plant Automata with Bisimulation Quotients. In: Glück, R., Santocanale, L., Winter, M. (eds) Relational and Algebraic Methods in Computer Science. RAMiCS 2023. Lecture Notes in Computer Science, vol 13896. Springer, Cham. https://doi.org/10.1007/978-3-031-28083-2_6
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DOI: https://doi.org/10.1007/978-3-031-28083-2_6
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