Abstract
Consider the problem of deciding whether a Boolean formula f is self-dual, i.e. f is logically equivalent to its dual formula f d, defined by f d(x)=¯f(¯x). This problem is a well-studied problem in several areas like theory of coteries, database theory, hypergraph theory or computational learning theory. In this paper we exhibit polynomial time algorithms for testing self-duality for several natural classes of formulas where the problem was not known to be solvable. Some of the results are obtained by means of a new characterization of self-dual formulas in terms of its Fourier spectrum.
Supported by the Esprit EC program under project 7141 (ALCOM-II) and the Spanish DGICYT (project PB92-0709).
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
D. Angluin, L. Hellerstein, and M. Karpinski. Learning read-once formulas with queries. J. ACM, 40:185–210, 1993.
J.C. Bioch and T. Ibaraki. Complexity of identification and dualization of positive Boolean functions. Information and Computation, 123:50–63, 1995.
C. Domingo. Exact learning of subclasses of cdnf formulas with membership queries. In Proc. of the 2nd International Conference on Computing and Combinatorics, COCOON, Lecture Notes in Computer Science, 1090:179–188, Springer-Verlag, 1996.
T. Eiter and G. Gottlob. Identifying the minimal transversals of a hypergraph and related problems. Technical Report CD-TR 91/16, Christial Doppler Labor Für Expertensysteme, Technische Universität Wien, 1991.
M. Fredman and L. Khachiyan. On the complexity of dualization of monotone disjunctive normal form. Technical Report LCSR-TR-225, Department of Computer Science, Rutgers University, May 1994.
H. Garcia-Molina and D. Barbara. How to assign votes in a distributed system. Journal of the Association for Computing Machinery, 32:841–860, 1985.
T. Ibaraki and T. Kameda. A theory of coteries: Mutual exclusion in distributed systems. IEEE Trans. on Parallel and Distributed Systems, pages 779–794, 1993.
J. Kahn, G. Kalai, and N. Linial. The influence of variables on Boolean functions. In Proc. 28th Annu. IEEE Sympos. Found. Comput. Sci., pages 68–80. IEEE Computer Society Press, Los Alamitos, CA, 1988.
E. Kushilevitz and Y. Mansour. Learning decision trees using the fourier spectrum. SIAM J. Comput., 22(6):1331–1348, 1993. Earlier version appeared in STOC 1991.
N. Linial, Y. Mansour, and N. Nisan. Constant depth circuits, Fourier transform and learnability. Journal of the Association for Computing Machinery, 40(3):607–620, 1993.
K. Makino and T. Ibaraki. A fast and simple algorithm for identifying 2-monotonic positive Boolean functions. Technical Report COMP94-46, IEICE, 1994.
K. Makino and T. Ibaraki. The maximum latency and identification of positive Boolean functions. In Proceedings of ISAAC'94, Algorithms and Computation, volume 834 of Lecture Notes in Computer Science, pages 324–332, 1994.
H. Mannila and K.J. Raïhä. Design by example: An application of Armstrong relations. Journal of Computer and System Sciences, 22:126–141, 1987.
J. Naor and M. Naor. Small-bias, probability spaces: Efficient constructions and applications. SIAM Journal on Computing, 22:838–856, 1993.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1997 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Domingo, C. (1997). Polynomial time algorithms for some self-duality problems. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_70
Download citation
DOI: https://doi.org/10.1007/3-540-62592-5_70
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-62592-6
Online ISBN: 978-3-540-68323-0
eBook Packages: Springer Book Archive