Horn minimization by iterative decomposition |
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Authors: | Endre Boros Ond?ej ?epek Alexander Kogan |
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Affiliation: | (1) RUTCOR, Rutgers University, 640 Bartholomew Road, Piscataway, NJ 08854-8003, USA;(2) Department of Theoretical Informatics, Charles University, Malostranské nám. 25, 118 00 Praha 1, Czech Republic;(3) Accounting and Information Systems, Faculty of Management, Rutgers University, Newark, NJ 07102, USA |
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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 off 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.
This revised version was published online in June 2006 with corrections to the Cover Date. |
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