Abstract
We present a uniform signature-based approach to compute the most popular bisimulations. Our approach is implemented symbolically using BDDs, which enables the handling of very large transition systems. Signatures for the bisimulations are built up from a few generic building blocks, which naturally correspond to efficient BDD operations. Thus, the definition of an appropriate signature is the key for a rapid development of algorithms for other types of bisimulation.
We provide experimental evidence of the viability of this approach by presenting computational results for many bisimulations on real-world instances. The experiments show cases where our framework can handle state spaces efficiently that are far too large to handle for any tool that requires an explicit state space description.
This work was partly supported by the German Research Council (DFG) as part of the Transregional Collaborative Research Center “Automatic Verification and Analysis of Complex Systems” (SFB/TR 14 AVACS). See www.avacs.org for more information.
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
Wimmer, R., Herbstritt, M., Becker, B.: Minimization of Large State Spaces using Symbolic Branching Bisimulation. In: Proc. of IEEE Workshop on Design & Diagnostics of Electronic Circuits & Systems (DDECS), pp. 9–14 (2006)
Chehaibar, G., et al.: Specification and Verification of the PowerScaleTM Bus Arbitration Protocol: An Industrial Experiment with LOTOS. In: Proc. of FORTE, vol. 69, pp. 435–450 (1996)
Giannakopoulou, D.: Model Checking for Concurrent Software Architectures. PhD thesis, Imperial College, University of London (1999)
Graf, S., Steffen, B., Luttgen, G.: Compositional minimisation of finite state systems using interface specifications. Formal Asp. of Comp. 8(5), 607–616 (1996)
Kanellakis, P., Smolka, S.: CCS expressions, finite state processes, and three problems of equivalence. Information and Computation 86(1), 43–68 (1990)
Paige, R., Tarjan, R.E.: Three partition refinement algorithms. SIAM Jour. on Computing 16(6), 973–989 (1987)
Burch, J., et al.: Symbolic Model Checking: 1020 States and Beyond. Information and Computation 98(2), 142–170 (1992)
Bouajjani, A., Fernandez, J.C., Halbwachs, N.: Minimal model generation. In: Clarke, E., Kurshan, R.P. (eds.) CAV 1990. LNCS, vol. 531, pp. 197–203. Springer, Heidelberg (1991)
Bouajjani, A., Fernandez, J.C., Halbwachs, N., Ratel, C., Raymond, P.: Minimal state graph generation. Science of Computer Programming 18, 247–269 (1992)
Bouali, A., de Simone, R.: Symbolic Bisimulation Minimisation. In: Probst, D.K., von Bochmann, G. (eds.) CAV 1992. LNCS, vol. 663, pp. 96–108. Springer, Heidelberg (1993)
Blom, S., Orzan, S.: Distributed Branching Bisimulation Reduction of State Spaces. ENTCS 89(1), 113–990 (2003)
Milner, R.: Communication and Concurrency. Prentice-Hall, Englewood Cliffs (1989)
Milner, R.: A Calculus of Communication Systems. LNCS, vol. 92. Springer, Heidelberg (1980)
Milner, R.: Lectures on a Calculus for Communicating Systems. In: Brookes, S.D., Winskel, G., Roscoe, A.W. (eds.) Seminar on Concurrency. LNCS, vol. 197, pp. 197–220. Springer, Heidelberg (1985)
van Glabbeek, R., Weijland, W.: Branching Time and Abstraction in Bisimulation Semantics. Journal of the ACM 43(3), 555–600 (1996)
Baeten, J., van Glabbeek, R.: Another Look at Abstraction in Process Algebra. In: Ottmann, T. (ed.) ICALP 1987. LNCS, vol. 267, pp. 84–94. Springer, Heidelberg (1987)
Bergstra, J.A., Ponse, A., van der Zwaag, M.B.: Branching time and orthogonal bisimulation equivalence. Theor. Comp. Sci. 309, 313–355 (2003)
Milner, R.: A Modal Characterization of Observable Machine-Behaviour. In: Astesiano, E., Böhm, C. (eds.) CAAP 1981. LNCS, vol. 112, pp. 25–34. Springer, Heidelberg (1981)
Montanari, U., Sassone, V.: Dynamic congruence vs. progressing bisimulation for CCS. Fundam. Inform. 16(1), 171–199 (1992)
Bouajjani, A., et al.: Safety for Branching Time Semantics. In: Leach Albert, J., Monien, B., Rodríguez-Artalejo, M. (eds.) ICALP 1991. LNCS, vol. 510, pp. 76–92. Springer, Heidelberg (1991)
van Glabbeek, R.J.: The linear time – branching time spectrum II. In: Best, E. (ed.) CONCUR 1993. LNCS, vol. 715, pp. 66–81. Springer, Heidelberg (1993)
Hermanns, H., Lohrey, M.: Priority and maximal progress are completely axiomatisable. In: Sangiorgi, D., de Simone, R. (eds.) CONCUR 1998. LNCS, vol. 1466, pp. 237–252. Springer, Heidelberg (1998)
Park, D.: Concurrency and automata on infinite sequences. In: Deussen, P. (ed.) GI-TCS 1981. LNCS, vol. 104, pp. 167–183. Springer, Heidelberg (1981)
Dovier, A., Gentilini, R., Piazza, C., Policriti, A.: Rank-based symbolic bisimulation (and model checking). ENTCS 67 (2002)
Klarlund, N.: An nlogn algorithm for online BDD refinement. In: Grumberg, O. (ed.) CAV 1997. LNCS, vol. 1254, pp. 107–118. Springer, Heidelberg (1997)
Somenzi, F.: CUDD: CU Decision Diagram Package Release 2.4.1. University of Colorado at Boulder (2005)
Groote, J.F., Vaandrager, F.W.: An Efficient Algorithm for Branching Bisimulation and Stuttering Equivalence. In: Paterson, M. (ed.) ICALP 1990. LNCS, vol. 443, pp. 626–638. Springer, Heidelberg (1990)
Bryant, R.: Graph-Based Algorithms for Boolean Function Manipulation. IEEE Trans. on Comp. 35(8), 677–691 (1986)
Wegener, I.: Branching programs and binary decision diagrams. SIAM Monographs on Discrete Mathematics and Applications. SIAM, Philadelphia (2000)
Strampp, K.: Symbolische Berechnung von Bisimulationen. Diploma thesis, Albert-Ludwigs-University Freiburg, Germany (2006)
Matsunaga, Y., McGeer, P.C., Brayton, R.K.: On computing the transitive closure of a state transition relation. In: Proc. of DAC, pp. 260–265. ACM Press, New York (1993)
Burch, J.R., et al.: Sequential circuit verification using symbolic model checking. In: Proc. of DAC, pp. 46–51. ACM Press, New York (1990)
Garavel, H., Hermanns, H.: On Combining Functional Verification and Performance Evaluation using CADP. In: Eriksson, L.-H., Lindsay, P.A. (eds.) FME 2002. LNCS, vol. 2391, Springer, Heidelberg (2002)
Fernandez, J.C., et al.: CADP: A Protocol Validation and Verification Toolbox. In: Alur, R., Henzinger, T.A. (eds.) CAV 1996. LNCS, vol. 1102, pp. 437–440. Springer, Heidelberg (1996)
Herbstritt, M., Wimmer, R., Peikenkamp, T., Böde, E., Adelaide, M., Johr, S., Hermanns, H., Becker, B.: Analysis of Large Safety-Critical Systems: A quantitative Approach. Reports of SFB/TR 14 AVACS 8 (2006) ISSN 1860-9821
Ciardo, G., Tilgner, M.: On the use of Kronecker operators for the solution of generalized stochastic Petri nets. Technical Report 96-35, ICASE (1996)
Kuntz, M., Siegle, M., Werner, E.: Symbolic Performance and Dependability Evaluation with the Tool CASPA. In: Núñez, M., Maamar, Z., Pelayo, F.L., Pousttchi, K., Rubio, F. (eds.) FORTE 2004. LNCS, vol. 3236, pp. 293–307. Springer, Heidelberg (2004)
Harel, D., Politi, M.: Modelling Reactive Systems with Statecharts: The Statemate Approach. McGraw-Hill, New York (1998)
ERTMS: Project (May 16, 2006), Website http://ertms.uic.asso.fr/etcs.html
ARP 4761: Guidelines and Methods for Conducting the Safety Assessment Process on Civil Airborne Systems and Equipment. Aerospace Recommended Practice, Society of Automotive Engineers, Detroit, USA (1996)
Hermanns, H.: Interactive Markov Chains: The Quest for Quantified Quality. In: Hermanns, H. (ed.) Interactive Markov Chains. LNCS, vol. 2428, Springer, Heidelberg (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2006 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Wimmer, R., Herbstritt, M., Hermanns, H., Strampp, K., Becker, B. (2006). Sigref – A Symbolic Bisimulation Tool Box. In: Graf, S., Zhang, W. (eds) Automated Technology for Verification and Analysis. ATVA 2006. Lecture Notes in Computer Science, vol 4218. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11901914_35
Download citation
DOI: https://doi.org/10.1007/11901914_35
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-47237-7
Online ISBN: 978-3-540-47238-4
eBook Packages: Computer ScienceComputer Science (R0)