Minimal representation of directed hypergraphs
SIAM Journal on Computing
Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Optimal compression of propositional Horn knowledge bases: complexity and approximation
Artificial Intelligence
Approximation of k-set cover by semi-local optimization
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Minimum Covers in Relational Database Model
Journal of the ACM (JACM)
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
The minimum equivalent DNF problem and shortest implicants
Journal of Computer and System Sciences
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
Horn minimization by iterative decomposition
Annals of Mathematics and Artificial Intelligence
Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression
IEEE Transactions on Knowledge and Data Engineering
The complexity of theorem-proving procedures
STOC '71 Proceedings of the third annual ACM symposium on Theory of computing
Graphs and Hypergraphs
Minimizing DNF Formulas and AC^0_d Circuits Given a Truth Table
CCC '06 Proceedings of the 21st Annual IEEE Conference on Computational Complexity
Boolean Functions
Analysis of Approximation Algorithms for k-Set Cover Using Factor-Revealing Linear Programs
Theory of Computing Systems
Exclusive and essential sets of implicates of Boolean functions
Discrete Applied Mathematics
A subclass of Horn CNFs optimally compressible in polynomial time
Annals of Mathematics and Artificial Intelligence
Approximating the unweighted k-set cover problem: greedy meets local search
WAOA'06 Proceedings of the 4th international conference on Approximation and Online Algorithms
Complexity of two-level logic minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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In this short note we introduce a hierarchy of classes of Boolean functions, where each class is defined by the minimum allowed length of prime implicants of the functions in the class. We show that for a given DNF and a given class in the hierarchy, it is possible to test in polynomial time whether the DNF represents a function from the given class. For the first class in the hierarchy we moreover present a polynomial time algorithm which for a given input DNF outputs a shortest logically equivalent DNF, i.e. a shortest DNF representation of the underlying function. This class is therefore a new member of a relatively small family of classes for which the Boolean minimization problem can be solved in polynomial time. For the second class and higher classes in the hierarchy we show that the Boolean minimization problem can be approximated within a constant factor.