Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Two-level logic minimization: an overview
Integration, the VLSI Journal
The Minimum Equivalent DNF Problem and Shortest Implicants
FOCS '98 Proceedings of the 39th Annual Symposium on Foundations of Computer Science
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Minimizing Disjunctive Normal Form Formulas and $AC^0$ Circuits Given a Truth Table
SIAM Journal on Computing
Query Learning and Certificates in Lattices
ALT '08 Proceedings of the 19th international conference on Algorithmic Learning Theory
On approximate horn formula minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
Construction and learnability of canonical Horn formulas
Machine Learning
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Given a Boolean function f, the quantity ess(f) denotes the largest set of assignments that falsify f, no two of which falsify a common implicate of f. Although ess(f) is clearly a lower bound on cnf_size(f) (the minimum number of clauses in a CNF formula for f), C@?epek et al. showed it is not, in general, a tight lower bound [6]. They gave examples of functions f for which there is a small gap between ess(f) and cnf_size(f). We demonstrate significantly larger gaps. We show that the gap can be exponential in n for arbitrary Boolean functions, and @Q(n) for Horn functions, where n is the number of variables of f. We also introduce a natural extension of the quantity ess(f), which we call ess"k(f), which is the largest set of assignments, no k of which falsify a common implicate of f.