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A subclass of Horn CNFs optimally compressible in polynomial time

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Abstract

The problem of Horn Minimization (HM) can be stated as follows: given a Horn CNF representing a Boolean function f, find a shortest possible (optimally compressed) CNF representation of f, i.e., a CNF representation of f which consists of the minimum possible number of clauses. This problem is the formalization of the problem of knowledge compression for speeding up queries to propositional Horn expert systems, and it is known to be NP-hard. There are two subclasses of Horn functions for which HM is known to be solvable in polynomial time: acyclic and quasi-acyclic Horn functions. In this paper we define a new class of Horn functions properly containing both of the known classes and design a polynomial time HM algorithm for this new class.

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Authors and Affiliations

  1. RUTCOR, Rutgers University, P. O. Box 5062, New Brunswick, NJ, 08903, USA

    Endre Boros & Alexander Kogan

  2. Department of Theoretical Computer Science and Mathematical Logic, Charles University, Malostranské nám. 25, 118 00, Praha 1, Czech Republic

    Ondřej Čepek & Petr Kučera

  3. Institute of Finance and Administration—VŠFS, Estonská 500, 100 00, Praha 10, Czech Republic

    Ondřej Čepek

  4. Department of Accounting and Information Systems, Rutgers Business School, Rutgers University, Newark, NJ, 07102, USA

    Alexander Kogan

Authors
  1. Endre Boros
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  2. Ondřej Čepek
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  3. Alexander Kogan
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  4. Petr Kučera
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Correspondence to Ondřej Čepek.

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Boros, E., Čepek, O., Kogan, A. et al. A subclass of Horn CNFs optimally compressible in polynomial time. Ann Math Artif Intell 57, 249–291 (2009). https://doi.org/10.1007/s10472-010-9197-7

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  • DOI: https://doi.org/10.1007/s10472-010-9197-7

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