Abstract
We investigate the complexity of enumerating pseudo-intents in the lectic order. We look at the following decision problem: Given a formal context and a set of n pseudo-intents determine whether they are the lectically first n pseudo-intents. We show that this problem is coNP-hard. We thereby show that there cannot be an algorithm with a good theoretical complexity for enumerating pseudo-intents in a lectic order. In a second part of the paper we introduce the notion of minimal pseudo-intents, i. e. pseudo-intents that do not strictly contain a pseudo-intent. We provide some complexity results about minimal pseudo-intents that are readily obtained from the previous result.
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References
Baader, F., Ganter, B., Sattler, U., Sertkaya, B.: Completing description logic knowledge bases using formal concept analysis. In: Proc. of the 20th Int. Joint Conf. on Artificial Intelligence (IJCAIÂ 2007). AAAI Press/The MIT Press (2007)
Eiter, T., Gottlob, G.: Hypergraph transversal computation and related problems. In: Flesca, S., Greco, S., Leone, N., Ianni, G. (eds.) JELIA 2002. LNCS (LNAI), vol. 2424, pp. 549–564. Springer, Heidelberg (2002)
Fredman, M.L., Khachiyan, L.: On the complexity of dualization of monotone disjunctive normal forms. Journal of Algorithms 21(3), 618–628 (1996)
Ganter, B.: Two basic algorithms in concept analysis. Preprint 831, Fachbereich Mathematik, TU Darmstadt, Darmstadt, Germany (1984)
Ganter, B., Wille, R.: Formal Concept Analysis: Mathematical Foundations. Springer, New York (1997)
Guigues, J.-L., Duquenne, V.: Familles minimales d’implications informatives résultant d’un tableau de données binaires. Math. Sci. Humaines 95, 5–18 (1986)
Kuznetsov, S.O.: On the intractability of computing the Duquenne-Guigues base. Journal of Universal Computer Science 10(8), 927–933 (2004)
Kuznetsov, S.O.: Counting pseudo-intents and #P-completeness. In: Missaoui, R., Schmidt, J. (eds.) Formal Concept Analysis. LNCS (LNAI), vol. 3874, pp. 306–308. Springer, Heidelberg (2006)
Kuznetsov, S.O., Obiedkov, S.A.: Algorithms for the construction of concept lattices and their diagram graphs. In: Siebes, A., De Raedt, L. (eds.) PKDD 2001. LNCS (LNAI), vol. 2168, pp. 289–300. Springer, Heidelberg (2001)
Obiedkov, S., Duquenne, V.: Attribute-incremental construction of the canonical implication basis. Annals of Mathematics and Artificial Intelligence 49(1-4), 77–99 (2007)
Sertkaya, B.: Some computational problems related to pseudo-intents. In: Ferré, S., Rudolph, S. (eds.) ICFCA 2009. LNCS (LNAI), vol. 5548, pp. 130–145. Springer, Heidelberg (2009)
Sertkaya, B.: Towards the complexity of recognizing pseudo-intents. In: Dau, F., Rudolph, S. (eds.) ICCS 2009. LNCS, vol. 5662, pp. 284–292. Springer, Heidelberg (2009)
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Distel, F. (2010). Hardness of Enumerating Pseudo-intents in the Lectic Order. In: Kwuida, L., Sertkaya, B. (eds) Formal Concept Analysis. ICFCA 2010. Lecture Notes in Computer Science(), vol 5986. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-11928-6_9
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DOI: https://doi.org/10.1007/978-3-642-11928-6_9
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