Abstract
We present an automatic technique for the detection of structural symmetry in a model directly from its Promela specification. Our approach involves finding the static channel diagram of the model, a graphical representation of channel-based system communication; computing the group of symmetries of this diagram; and computing the largest possible subgroup of these symmetries which induce automorphisms of the underlying model. We describe a tool, SymmExtractor, which, for a given model and LTL property, uses our approach to find a group of symmetries of the model which preserve the property. This group can then be used for symmetry reduction during model checking using existing quotient-based methods. Unlike previous approaches, our method can detect arbitrary structural symmetries arising from the communication structure of the model.
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
Aloul, F., Ramani, A., Markov, I., Sakallah, K.: Solving difficult SAT instances in the presence of symmetry. IEEE Transactions on Computer Aided Design 22(9), 1117–1137 (2003)
Balasubramanian, J., Schmidt, D., Dowdy, L., Othman, O.: Evaluating the performance of middleware load balancing strategies. In: EDOC 2001, pp. 135–146. IEEE Computer Society Press, Los Alamitos (2004)
Bosnacki, D., Dams, D., Holenderski, L.: Symmetric Spin. International Journal on Software Tools for Technology Transfer 4(1), 65–80 (2002)
Calder, M., Miller, A.: Generalising feature interactions in email. In: Feature Interactions in Telecommunications and Software Systems VII, pp. 187–205. IOS Press, Amsterdam (2003)
Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. The MIT Press, Cambridge (1999)
Clarke, E., Emerson, E., Jha, S., Sistla, A.: Symmetry reductions in model-checking. In: Y. Vardi, M. (ed.) CAV 1998. LNCS, vol. 1427, pp. 147–158. Springer, Heidelberg (1998)
Clarke, E., Enders, R., Filkhorn, T., Jha, S.: Exploiting symmetry in temporal logic model checking. Formal Methods in System Design 9(1–2), 77–104 (1996)
Clarke, E., Grumberg, O., Long, D.: Model checking and abstraction. In: POPL 1992, pp. 343–354. ACM Press, New York (1992)
Darga, P.T., Liffiton, M.H., Sakallah, K.A., Markov, I.L.: Exploiting structure in symmetry detection for CNF. In: DAC 2004, pp. 530–534. ACM Press, New York (2004)
Derepas, F., Gastin, P.: Model checking systems of replicated processes with Spin. In: Dwyer, M.B. (ed.) SPIN 2001. LNCS, vol. 2057, pp. 235–251. Springer, Heidelberg (2001)
Donaldson, A., Miller, A., Calder, M.: Finding symmetry in models of concurrent systems by static channel diagram analysis. In: AVoCS 2004. ENTCS, vol. 128(6), pp. 161–177. Elsevier Science Publishers, Amsterdam (2005)
Gagnon, E., Hendren, L.J.: SableCC, an object-oriented compiler framework. In: TOOLS 1998, pp. 140–154. IEEE Computer Society Press, Los Alamitos (1998)
The Gap Group. GAP–Groups Algorithms and Programming, Version 4.2. Aachen, St. Andrews (1999), http://www-gap.dcs.st-and.ac.uk/~gap
Holzmann, G.J.: The SPIN model checker: primer and reference manual. Addison-Wesley, Reading (2003)
Ip, C., Dill, D.: Better verification through symmetry. Formal Methods in System Design 9, 41–75 (1996)
Rose, J.: A Course in Group Theory. Dover Publications, Mineola (1964)
Sistla, A.P., Godefroid, P.: Symmetry and reduced symmetry in model checking. ACM Transactions on Programming Languages and Systems 25(4), 702–734 (2004)
Tanenbaum, A.S., van Steen, M.: Distributed Systems Principles and Paradigms. Prentice-Hall, Englewood Cliffs (2002)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Donaldson, A.F., Miller, A. (2005). Automatic Symmetry Detection for Model Checking Using Computational Group Theory. In: Fitzgerald, J., Hayes, I.J., Tarlecki, A. (eds) FM 2005: Formal Methods. FM 2005. Lecture Notes in Computer Science, vol 3582. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11526841_32
Download citation
DOI: https://doi.org/10.1007/11526841_32
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27882-5
Online ISBN: 978-3-540-31714-2
eBook Packages: Computer ScienceComputer Science (R0)