Abstract
We present a trajectory-based model for describing hybrid systems. For this we use left quantales and left semirings, thus providing a new application for these algebraic structures. Furthermore, we sketch a connection between game theory and hybrid systems.
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References
Backhouse, R., Michaelis, D.: Fixed-Point Characterisation of Winning Strategies in Impartial Games. In: Berghammer, R., Möller, B., Struth, G. (eds.) RelMiCS 2003. LNCS, vol. 3051, pp. 34–47. Springer, Heidelberg (2004)
Cohen, E.: Separation and Reduction. In: Backhouse, R., Oliveira, J.N. (eds.) MPC 2000. LNCS, vol. 1837, pp. 45–59. Springer, Heidelberg (2000)
Conway, J.H.: Regular Algebra and Finite Machines. Chapman & Hall, Boca Raton (1971)
Davoren, J.M., Nerode, A.: Logics for Hybrid Systems. Proc. IEEE 88, 985–1010 (2000)
Desharnais, J., Möller, B., Struth, G.: Kleene Algebra with Domain. ACM Trans. Computational Logic (to appear, 2006); Preliminary version: Universität Augsburg, Institut für Informatik, Report No. 2003-07 (June 2003)
Desharnais, J., Möller, B., Struth, G.: Modal Kleene Algebra and Applications – A Survey. J. Relational Methods in Computer Science 1, 93–131 (2004), http://www.cosc.brocku.ca/Faculty/Winter/JoRMiCS/
Henzinger, T.: The Theory of Hybrid Automata. In: Proc. 11th Annual IEEE Symposium on Logic in Computer Science, New Brunswick, New Jersey, pp. 278–292 (1996)
Höfner, P.: From Sequential Algebra to Kleene Algebra: Interval Modalities and Duration Calculus. Technical Report 2005-5, Institut für Informatik, Universität Augsburg (2005)
Höfner, P.: An Algebraic Semantics for Duration Calculus. In: 17th European Summer School in Logic, Language and Information (ESSLLI), Proc. 10th ESSLLI Student Session, Heriot-Watt University Edinburgh, Scotland, August 2005, pp. 99–111 (2005)
Isaacs, R.: Differential Games. Wiley, Chichester (1965) Republished: Dover (1999)
von Karger, B.: Temporal Algebra. Habilitation thesis, University of Kiel (1997)
Kozen, D.: Kleene Algebra with Tests. ACM Trans. Programming Languages and Systems 19, 427–443 (1997)
Lynch, N.A., Segala, R., Vaandrager, F.W.: Hybrid I/O Automata. Information and Computation 185, 105–157 (2003)
Möller, B.: Complete Tests do not Guarantee Domain. Technical Report 2005-6, Institut für Informatik, Universität Augsburg (2005)
Möller, B.: Lazy Kleene Algebra. In: Kozen, D. (ed.) MPC 2004. LNCS, vol. 3125, pp. 252–273. Springer, Heidelberg (2004)
Sintzoff, M.: Iterative Synthesis of Control Guards Ensuring Invariance and Inevitability in Discrete-Decision Games. In: Owe, O., Krogdahl, S., Lyche, T. (eds.) From Object-Orientation to Formal Methods. LNCS, vol. 2635, pp. 272–301. Springer, Heidelberg (2004)
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Höfner, P., Möller, B. (2006). Towards an Algebra of Hybrid Systems. In: MacCaull, W., Winter, M., Düntsch, I. (eds) Relational Methods in Computer Science. RelMiCS 2005. Lecture Notes in Computer Science, vol 3929. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11734673_10
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DOI: https://doi.org/10.1007/11734673_10
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-33339-5
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