Horn minimization by iterative decomposition

  • Authors:

  • Endre Boros;Ondřej Čepek;Alexander Kogan

  • Affiliations:

  • RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854‐8003, USA E-mail: boros@rutcor.rutgers.edu;Department of Theoretical Informatics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic E-mail: cepek@ksi.ms.mff.cuni.cz;Accounting and Information Systems, Faculty of Management, Rutgers University, Newark, NJ 07102, USA E-mail: kogan@rutcor.rutgers.edu

  • Venue:
  • Annals of Mathematics and Artificial Intelligence
  • Year:
  • 1998

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Abstract

Given a Horn CNF representing a Boolean function f, the problem of Horn minimization consists in constructing a CNF representation of f which has a 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. In this paper we present a linear time algorithm which takes a Horn CNF as an input, and through a series of decompositions reduces the minimization of the input CNF to the minimization problem on a “shorter” CNF. The correctness of this decomposition algorithm rests on several interesting properties of Horn functions which, as we prove here, turn out to be independent of the particular CNF representations.