Abstract
Probabilistic timed automata are an extension of timed automata with discrete probability distributions. Simulation and bisimulation relations are widely-studied in the context of the analysis of system models, with applications in the stepwise development of systems and in model reduction. In this paper, we study probabilistic timed simulation and bisimulation relations for probabilistic timed automata. We present an EXPTIME algorithm for deciding whether two probabilistic timed automata are probabilistically timed similar or bisimilar. Furthermore, we consider a logical characterization of probabilistic timed bisimulation.
Supported in part by the MIUR-PRIN project PaCo - Performability-Aware Computing: Logics, Models and Languages.
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References
Alur, R., Dill, D.L.: A theory of timed automata. TCS 126(2), 183–235 (1994)
Puterman, M.L.: Markov Decision Processes. J. Wiley & Sons, Chichester (1994)
Segala, R., Lynch, N.A.: Probabilistic simulations for probabilistic processes. Nordic Journal of Computing 2(2), 250–273 (1995)
Segala, R.: Modeling and Verification of Randomized Distributed Real-Time Systems. PhD thesis, Massachusetts Institute of Technology (1995)
Kwiatkowska, M., Norman, G., Segala, R., Sproston, J.: Automatic verification of real-time systems with discrete probability distributions. TCS 286, 101–150 (2002)
Kwiatkowska, M., Norman, G., Sproston, J.: Probabilistic model checking of deadline properties in the IEEE 1394 FireWire root contention protocol. Formal Aspects of Computing 14(3), 295–318 (2003)
Kwiatkowska, M., Norman, G., Parker, D., Sproston, J.: Performance analysis of probabilistic timed automata using digital clocks. FMSD 29, 33–78 (2006)
Milner, R.: An algebraic definition of simulation between programs. In: Proc. IJCAI’71, pp. 481–489. William Kaufmann, San Francisco (1971)
Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
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)
Taşıran, S., Alur, R., Kurshan, R.P., Brayton, R.K.: Verifying abstractions of timed systems. In: Sassone, V., Montanari, U. (eds.) CONCUR 1996. LNCS, vol. 1119, pp. 546–562. Springer, Heidelberg (1996)
Bozzelli, L., Legay, A., Pinchinat, S.: On timed alternating simulation for concurrent timed games. In: Proc. FSTTCS’09. LIPIcs, vol. 4, pp. 85–96. Schloss Dagstuhl–Leibniz-Zentrum fuer Informatik (2009)
Baier, C., Engelen, B., Majster-Cederbaum, M.E.: Deciding bisimilarity and similarity for probabilistic processes. JCSS 60(1), 187–231 (2000)
Zhang, L., Hermanns, H., Eisenbrand, F., Jansen, D.N.: Flow faster: Efficient decision algorithms for probabilistic simulations LMCS 4(4) (2008)
Holmer, U., Larsen, K.G., Yi, W.: Deciding properties of regular real time processes. In: Larsen, K.G., Skou, A. (eds.) CAV 1991. LNCS, vol. 575, pp. 443–453. Springer, Heidelberg (1992)
Hennessy, M., Milner, R.: Algebraic laws for nondeterminism and concurrency. JACM 32(1), 137–161 (1985)
Parma, A., Segala, R.: Logical characterizations of bisimulations for discrete probabilistic systems. In: Seidl, H. (ed.) FOSSACS 2007. LNCS, vol. 4423, pp. 287–301. Springer, Heidelberg (2007)
Jensen, H.E., Gregersen, H.: Formal design of reliable real time systems. Master’s thesis, Aalborg University (1995)
Jensen, H.E.: Model checking probabilistic real time systems. In: Proc. of the 7th Nordic Work. on Progr. Theory, pp. 247–261. Chalmers Institute of Technology (1996)
Yamane, S.: Probabilistic timed simulation verification and its application to stepwise refinement of real-time systems. In: Saraswat, V.A. (ed.) ASIAN 2003. LNCS, vol. 2896, pp. 276–290. Springer, Heidelberg (2003)
Chen, T., Han, T., Katoen, J.P.: Time-abstracting bisimulation for probabilistic timed automata. In: Proc. TASE’08, pp. 177–184. IEEE, Los Alamitos (2008)
Jonsson, B., Larsen, K.G.: Specification and refinement of probabilistic processes. In: Proc. LICS’91, pp. 266–277. IEEE, Los Alamitos (1991)
Laroussinie, F., Schnoebelen, P.: The state explosion problem from trace to bisimulation equivalence. In: Tiuryn, J. (ed.) FOSSACS 2000. LNCS, vol. 1784, pp. 192–207. Springer, Heidelberg (2000)
Laroussinie, F., Larsen, K.G., Weise, C.: From timed automata to logic – and back. In: Hájek, P., Wiedermann, J. (eds.) MFCS 1995. LNCS, vol. 969, pp. 529–539. Springer, Heidelberg (1995)
Aceto, L., Laroussinie, F.: Is your model checker on time? On the complexity of model checking for timed modal logics. JLAP 52-53, 7–51 (2000)
Sproston, J.: Model checking for probabilistic timed and hybrid systems. PhD thesis, University of Birmingham (2000)
Lanotte, R., Maggiolo-Schettini, A., Troina, A.: Weak bisimulation for probabilistic timed automata and applications to security. In: Proc. SEFM’03, pp. 34–43. IEEE, Los Alamitos (2003)
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Sproston, J., Troina, A. (2010). Simulation and Bisimulation for Probabilistic Timed Automata. In: Chatterjee, K., Henzinger, T.A. (eds) Formal Modeling and Analysis of Timed Systems. FORMATS 2010. Lecture Notes in Computer Science, vol 6246. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15297-9_17
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DOI: https://doi.org/10.1007/978-3-642-15297-9_17
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