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Towards the Complexity of Recognizing Pseudo-intents

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Conceptual Structures: Leveraging Semantic Technologies (ICCS 2009)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 5662))

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Abstract

Pseudo-intents play a key rôle in Formal Concept Analysis. They are the premises of the implications in the Duquenne-Guigues Base, which is a minimum cardinality base for the set of implications that hold in a formal context. It has been shown that checking whether a set is a pseudo-intent is in conp. However, it is still open whether this problem is conp-hard, or it is solvable in polynomial time. In the current work we prove a first lower bound for this problem by showing that it is at least as hard as transversal hypergraph, which is the problem of identifying the minimal transversals of a given hypergraph. This is a prominent open problem in hypergraph theory that is conjectured to form a complexity class properly contained between p and conp. Our result explains why the attempts to find a polynomial algorithm for recognizing pseudo-intents have failed until now. We also formulate a decision problem, namely first pseudo-intent, and show that if this problem is not polynomial, then, unless p = np, pseudo-intents cannot be enumerated with polynomial delay in a specified lexicographic order.

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Author information

Authors and Affiliations

  1. TU Dresden, Germany

    Barış Sertkaya

Authors
  1. Barış Sertkaya
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Editors and Affiliations

  1. Institut AIFB, Universität Karlsruhe (TH), 76128, Karlsruhe, Germany

    Sebastian Rudolph

  2. SAP Research Center CEC Dresden, Chemnitzer Strasse 48, 01187, Dresden, Germany

    Frithjof Dau

  3. Higher School of Economics, Department of Applied Mathematics and Information Science, State University, Kirpichnaya 33/5, 105679, Moscow, Russia

    Sergei O. Kuznetsov

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Sertkaya, B. (2009). Towards the Complexity of Recognizing Pseudo-intents. In: Rudolph, S., Dau, F., Kuznetsov, S.O. (eds) Conceptual Structures: Leveraging Semantic Technologies. ICCS 2009. Lecture Notes in Computer Science(), vol 5662. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-03079-6_22

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  • DOI: https://doi.org/10.1007/978-3-642-03079-6_22

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-03078-9

  • Online ISBN: 978-3-642-03079-6

  • eBook Packages: Computer ScienceComputer Science (R0)

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