Abstract
This paper presents a novel algorithm to compute weak bisimulation quotients for finite acyclic models. It is developed in the setting of interactive Markov chains, a model overarching both labelled transition systems and continuous-time Markov chains. This model has lately been used to give an acyclic compositional semantics to dynamic fault trees, a reliability modelling formalism.
While the theoretical complexity does not change substantially, the algorithm performs very well in practice, almost linear in the size of the input model. We use a number of case studies to show that it is vastly more efficient than the standard bisimulation minimisation algorithms. In particular we show the effectiveness in the analysis of dynamic fault trees.
This work is supported by the DFG as part of the Transregional Collaborative Research Center SFB/TR 14 AVACS and by the European Commission under the IST framework 7 project QUASIMODO.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
Blom, S., Fokkink, W., Groote, J.F., van Langevelde, I., Lisser, B., van de Pol, J.: μcrl: A toolset for analysing algebraic specifications. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 250–254. Springer, Heidelberg (2001)
Blom, S., Orzan, S.: Distributed branching bisimulation reduction of state spaces. Electr. Notes Theor. Comput. Sci. 89(1) (2003)
Böde, E., Herbstritt, M., Hermanns, H., Johr, S., Peikenkamp, T., Pulungan, R., Wimmer, R., Becker, B.: Compositional performability evaluation for statemate. In: QEST, pp. 167–178 (2006)
Boudali, H., Crouzen, P., Stoelinga, M.: A compositional semantics for dynamic fault trees in input/output interactive markov chains. In: ATVA, pp. 441–456 (2007)
Bravetti, M.: Revisiting interactive markov chains. Electronic Notes in Theoretical Computer Science 68(5) (2002)
Coppersmith, D., Winograd, S.: Matrix multiplication via arithmetic progressions. In: ACM Symposium on Theory of Computing (1987)
Coste, N., Garavel, H., Hermanns, H., Hersemeule, R., Thonnart, Y., Zidouni, M.: Quantitative evaluation in embedded system design: Validation of multiprocessor multithreaded architectures. In: DATE (2008)
Crouzen, P., Hermanns, H., Zhang, L.: No Cycling? Go Faster! On the minimization of acyclic models. Reports of SFB/TR 14 AVACS 41, SFB/TR 14 AVACS (July 2008), http://www.avacs.org ISSN: 1860-9821
Dovier, A., Piazza, C., Policriti, A.: A fast bisimulation algorithm. In: Berry, G., Comon, H., Finkel, A. (eds.) CAV 2001. LNCS, vol. 2102, pp. 79–90. Springer, Heidelberg (2001)
Dugan, J., Bavuso, S., Boyd, M.: Dynamic fault-tree models for fault-tolerant computer systems. IEEE Transactions on Reliability 41(3), 363–377 (1992)
Fokkink, W., Pang, J., van de Pol, J.: Cones and foci: A mechanical framework for protocol verification. Formal Methods in System Design 29(1), 1–31 (2006)
Garavel, H., Lang, F., Mateescu, R., Serwe, W.: Cadp 2006: A toolbox for the construction and analysis of distributed processes. In: CAV (2006)
Goralcikova, A., Koubek, V.: A reduct-and-closure algorithm for graphs. Mathematical Foundations of Computer Science 74, 301–307 (1979)
Griffioen, W.O.D., Vaandrager, F.W.: A theory of normed simulations. ACM Trans. Comput. Log. 5(4), 577–610 (2004)
Groote, J.F., Vaandrager, F.: An efficient algorithm for branching bisimulation and stuttering equivalence. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443. Springer, Heidelberg (1990)
Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. LNCS, vol. 2428. Springer, Heidelberg (2002)
Katoen, J.-P., Kemna, T., Zapreev, I.S., Jansen, D.N.: Bisimulation minimisation mostly speeds up probabilistic model checking. In: Grumberg, O., Huth, M. (eds.) TACAS 2007. LNCS, vol. 4424, pp. 87–101. Springer, Heidelberg (2007)
Lang, F.: Refined interfaces for compositional verification. In: Najm, E., Pradat-Peyre, J.-F., Donzeau-Gouge, V.V. (eds.) FORTE 2006. LNCS, vol. 4229, pp. 159–174. Springer, Heidelberg (2006)
Lynch, N., Tuttle, M.: An introduction to input/output automata. CWI Quarterly 2(3), 219–246 (1989)
Mateescu, R.: Local model-checking of modal mu-calculus on acyclic labeled transition systems. In: Katoen, J.-P., Stevens, P. (eds.) TACAS 2002. LNCS, vol. 2280, pp. 281–295. Springer, Heidelberg (2002)
Milner, R.: Communication and Concurrency. Prentice Hall, Englewood Cliffs (1989)
Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM J. Comput. 16(6), 973–989 (1987)
Simon, K.: An improved algorithm for transitive closure on acyclic digraphs. In: Kott, L. (ed.) ICALP 1986. LNCS, vol. 226, pp. 376–386. Springer, Heidelberg (1986)
Vesely, W., Goldberg, F., Roberts, N., Haasl, D.: Fault Tree Handbook. NASA (1981)
Wimmer, R., Herbstritt, M., Hermanns, H., Strampp, K., Becker, B.: Sigref- a symbolic bisimulation tool box. In: ATVA, pp. 477–492 (2006)
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 2008 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Crouzen, P., Hermanns, H., Zhang, L. (2008). On the Minimisation of Acyclic Models. In: van Breugel, F., Chechik, M. (eds) CONCUR 2008 - Concurrency Theory. CONCUR 2008. Lecture Notes in Computer Science, vol 5201. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-85361-9_25
Download citation
DOI: https://doi.org/10.1007/978-3-540-85361-9_25
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-85360-2
Online ISBN: 978-3-540-85361-9
eBook Packages: Computer ScienceComputer Science (R0)