Abstract
The problem of determining whether a monotone boolean function is self-dual has numerous applications in Logic and AI. The applications include theory revision, model-based diagnosis, abductive explanations and learning monotone boolean functions. It is not known whether self-duality of monotone boolean functions can be tested in polynomial time, though a quasi-polynomial time algorithm exists. We describe another quasi-polynomial time algorithm for solving the self-duality problem of monotone boolean functions and analyze its average-case behaviour on a set of randomly generated instances.
This is a preview of subscription content, log in via an institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Bioch, J., Ibaraki, T.: Complexity of identification and dualization of positive boolean functions. Information and Computation 123(1), 50–63 (1995)
Bioch, J., Ibaraki, T.: Decomposition of positive self-dual functions. Discrete Mathematics 140, 23–46 (1995)
Bioch, J.C., Ibaraki, T.: Generating and approximating nondominated coteries. IEEE Transactions on parallel and distributed systems 6(9), 905–913 (1995)
Bollobas, B.: Random Graphs. Academic Press, London (1985)
Boros, E., Hammer, P.L., Ibaraki, T., Kawakami, K.: Polynomial-time recognition of 2-monotonic positive boolean functions given by an oracle. SIAM Journal on Computing 26(1), 93–109 (1997)
Boros, E., Gurvich, V., Khachiyan, L., Makino, K.: On the complexity of generating maximal frequent and minimal infrequent sets. In: Alt, H., Ferreira, A. (eds.) STACS 2002. LNCS, vol. 2285, pp. 133–141. Springer, Heidelberg (2002)
de Kleer, J., Williams, B.C.: Diagnosing multiple faults. Artificial Intelligence 32, 97–130 (1987)
Domingo, C., Mishra, N., Pitt, L.: Efficient Read-Restricted Monotone CNF/DNF Dualization by Learning with Membership Queries. Machine Learning 37(1), 89–110 (1999)
Eiter, T., Gottlob, G.: Identifying the minimum transversals of a hypergraph and related problems. Siam Journal of Computing 24(6), 1278–1304 (1995)
Eiter, T., Gottlob, G.: Hypergraph Transversal Computation and Related Problems in Logic and AI. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 549–564. Springer, Heidelberg (2002)
Eiter, T., Makino, K.: On computing all abductive explanations. In: Proceeding 18th National Conference on Artificial Intelligence, AAAI 2002, pp. 62–67 (2002)
Feller, W.: Introduction to Probability Theory and its Applications, 3rd edn. John Wiley and Sons, Chichester (1967)
Franco, J.: On the probabilistic performance of the algorithms for the satisfiability problem. Information Processing Letters, 103–106 (1986)
Fredman, M.L., Khachiyan, L.: On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms 21(3), 618–628 (1996)
Garcia-Molina, H., Barbara, D.: How to assign votes in a distributed system. Journal of the ACM 32, 841–860 (1985)
Gaur, D., Krishnamurti, R.: Self-duality of bounded monotone boolean functions and related problems. In: The Eleventh Conference on Algorithmic Learning Theory. Lecture Notes in Computer Science (subseries LNAI), pp. 209–223 (2000)
Gunopulos, D., Khardon, R., Mannila, H., Toivonen, H.: Data mining, Hypergraph Transversals, and Machine Learning. In: Proc. Symposium on Principles of Database Systems, pp. 209–216 (1997)
Goldberg, A., Purdom, P., Brown, C.: Average time analysis for simplified davisputnam procedures. Information Processing Letters 15(2), 72–75 (1982)
Gurvich, V., Khachiyan, L.: Generating the irredundant conjunctive and disjunctive normal forms of monotone boolean functions. Technical Report LCSR-TR-251, Dept. of Computer Science, Rutgers Univ. (August 1995)
Ibaraki, T., Kameda, T.: A boolean theory of coteries. IEEE Transactions on Parallel and Distributed Systems, 779–794 (1993)
Eiter, T., Gottlob, G., Makino, K.: New results on monotone dualization and generating hypergraph transversals. In: Proceedings of the 34th Annual ACM Symposium on Theory of Computing, pp. 14–22 (2002)
Makino, K.: Studies on Positive and Horn Boolean Functions with Applications to Data Analysis. PhD thesis, Kyoto University (March 1997)
Makino, K.: Efficient dualization of O(log n) term disjunctive normal forms. Discrete Applied Mathematics 126(2-3), 305–312 (2003)
Makino, K., Ibaraki, T.: The maximum latency and identification of positive boolean functions. In: Du, D.-Z., Zhang, X.-S. (eds.) ISAAC 1994. LNCS, vol. 834, pp. 324–332. Springer, Heidelberg (1994)
Mannila, H., Räihä, K.J.: An application of armstrong relations. Journal of Computer and System Science 22, 126–141 (1986)
Purdom, P.W., Brown, C.A.: The pure literal rule and polynomial average time. SIAM Journal on Computing 14, 943–953 (1985)
Reiter, R.: A theory of diagnosis from first principles. Artificial Intelligence 32, 57–95 (1987)
Wendt, P.D., Coyle, E.J., Gallagher Jr., N.C.: Stack filters. IEEE Transactions on Acoustics, Speech and Signal Processing 34(4), 898–911
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
Gaur, D.R., Krishnamurti, R. (2004). Average Case Self-Duality of Monotone Boolean Functions. In: Tawfik, A.Y., Goodwin, S.D. (eds) Advances in Artificial Intelligence. Canadian AI 2004. Lecture Notes in Computer Science(), vol 3060. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-24840-8_23
Download citation
DOI: https://doi.org/10.1007/978-3-540-24840-8_23
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-22004-6
Online ISBN: 978-3-540-24840-8
eBook Packages: Springer Book Archive