Abstract
Probabilistic techniques for verification of finite-state transition systems offer huge memory savings over deterministic techniques. The two leading probabilistic schemes are hash compaction and the bitstate method, which stores states in a Bloom filter. Bloom filters have been criticized for being slow, inaccurate, and memory-inefficient, but in this paper, we show how to obtain Bloom filters that are simultaneously fast, accurate, memory-efficient, scalable, and flexible. The idea is that we can introduce large dependences among the hash functions of a Bloom filter with almost no observable effect on accuracy, and because computation of independent hash functions was the dominant computational cost of accurate Bloom filters and model checkers based on them, our savings are tremendous. We present a mathematical analysis of Bloom filters in verification in unprecedented detail, which enables us to give a fresh comparison between hash compaction and Bloom filters. Finally, we validate our work and analyses with extensive testing using 3SPIN, a model checker we developed by extending SPIN.
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
Bloom, B.H.: Space/time trade-offs in hash coding with allowable errors. Communications of the ACM 13(7), 422–426 (1970)
Broder, A., Mitzenmacher, M.: Network applications of Bloom filters: A survey. In: Proc. of the 40th Annual Allerton Conference on Communication, Control, and Computing, pp. 636–646 (2002)
Ip, C.N., Dill, D.L.: Better verification through symmetry. In: Computer Hardware Description Languages and their Applications, Ottawa, Canada, pp. 87–100. Elsevier Science Publishers B.V, Amsterdam (1993)
Cormen, T.H., Stein, C., Rivest, R.L., Leiserson, C.E.: Introduction to Algorithms. McGraw-Hill Higher Education, New York (2001)
Dillinger, P.C., Manolios, P.: Fast and accurate bitstate verification for SPIN. In: 11th SPIN Workshop, Barcelona, Spain (April 2004)
Clarke, E.M., Filkorn, T., Jha, S.: Exploiting symmetry in temporal logic model checking. In: Courcoubetis, C. (ed.) CAV 1993. LNCS, vol. 697, pp. 450–461. Springer, Heidelberg (1993)
Emerson, F.A., Sistla, A.P.: Symmetry and model checking. Formal Methods in System Design: An International Journal 9(1/2), 105–131 (1996)
Fan, L., Cao, P., Almeida, J., Broder, A.Z.: Summary cache: a scalable wide-area Web cache sharing protocol. IEEE/ACM Transactions on Networking 8(3), 281–293 (2000)
Godefroid, P., Wolper, P.: A partial approach to model checking. In: Logic in Computer Science, pp. 406–415 (1991)
Gonnet, G.H.: Handbook of Algorithms and Data Structures. Addison-Wesley, Reading (1984)
Holzmann, G., Peled, D.: Partial order reduction of the state space. In: First SPIN Workshop, Montr‘eal, Quebec (1995)
Holzmann, G.J.: Design and Validation of Computer Protocols. Prentice-Hall, Englewood Cliffs (1991)
Holzmann, G.J.: An analysis of bitstate hashing. In: Proc. 15th Int. Conf on Protocol Specification, Testing, and Verification, INWG/IFIP, Warsaw, Poland, pp. 301–314. Chapman and Hall, Boca Raton (1995)
Holzmann, G.J.: The Spin Model Checker: Primer and Reference Manual. Addison-Wesley, Boston (2003)
Knuth, D.E.: The Art of Computer Programming, Sorting and Searching, 2nd edn., vol. 3. Addison Wesley Longman Publishing Co., Inc, Amsterdam (1997)
Mitzenmacher, M.: Compressed Bloom filters. In: Proc. of the 20th Annual ACM Symposium on Principles of Distributed Computing, IEEE/ACM Trans. on Net., pp. 144–150 (2001)
Penna, G., Intrigila, B., Tronci, E., Zilli, M.: Exploiting transition locality in the disk based Murphi verifier. In: 4th International Conference on Formal Methods in Computer Aided Verification, pp. 202–219 (2002)
Stern, U., Dill, D.L.: Improved probabilistic verification by hash compaction. In: Camurati, P.E., Eveking, H. (eds.) CHARME 1995. LNCS, vol. 987, pp. 206–224. Springer, Heidelberg (1995)
Stern, U., Dill, D.L.: A new scheme for memory-efficient probabilistic verification. In: IFIP TC6/WG6.1 Joint International Conference on Formal Description Techniques for Distributed Systems and Communication Protocols, and Protocol Specification, Testing, and Verification, pp. 333–348, Kaiserslautern Germany, October 8-11 (1996)
Visser, W., Havelund, K., Brat, G., Park, S.: Model checking programs. In: International Conference on Automated Software Engineering (September 2000)
Wolper, P., Leroy, D.: Reliable hashing without collision detection. In: 5th International Conference on Computer Aided Verification, pp. 59–70 (1993)
Wolper, P., Stern, U., Leroy, D., Dill, D.: Reliable probabilistic verification using hash compaction, Unpublished
Yu, Y., Manolios, P., Lamport, L.: Model checking TLA+ specifications. In: Pierre, L., Kropf, T. (eds.) CHARME 1999. LNCS, vol. 1703, pp. 54–66. Springer, Heidelberg (1999)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2004 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Dillinger, P.C., Manolios, P. (2004). Bloom Filters in Probabilistic Verification. In: Hu, A.J., Martin, A.K. (eds) Formal Methods in Computer-Aided Design. FMCAD 2004. Lecture Notes in Computer Science, vol 3312. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-30494-4_26
Download citation
DOI: https://doi.org/10.1007/978-3-540-30494-4_26
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-23738-9
Online ISBN: 978-3-540-30494-4
eBook Packages: Springer Book Archive