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.
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