DIMACS TR: 97-34

Horn Minimization by Iterative Decomposition

Authors:Endre Boros, Ondrej Cepek and Alexander Kogan


The problem of Horn minimization can be stated as follows: given a Horn CNF representing a Boolean function $f$, find a CNF representation of $f$ which consists of 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.

Paper Available at: ftp://dimacs.rutgers.edu/pub/dimacs/TechnicalReports/TechReports/1997/97-34.ps.gz
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