Minimal representation of directed hypergraphs
SIAM Journal on Computing
Logical foundations of artificial intelligence
Logical foundations of artificial intelligence
Unification as a complexity measure for logic programming
Journal of Logic Programming
Information Processing Letters
Information Processing Letters
Optimal compression of propositional Horn knowledge bases: complexity and approximation
Artificial Intelligence
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
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
On approximate horn formula minimization
ICALP'10 Proceedings of the 37th international colloquium conference on Automata, languages and programming
The complexity of Boolean formula minimization
Journal of Computer and System Sciences
Complexity of two-level logic minimization
IEEE Transactions on Computer-Aided Design of Integrated Circuits and Systems
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A CNF is minimal if no shorter CNF representing the same function exists, where by CNF length we mean either the number of clauses or the total number of literals (sum of clause lengths). In this paper we develop a decomposition approach that can be in certain situations applied to a CNF formula when proving its minimality. We give two examples in which this decomposition approach is used. Both examples deal with pure Horn minimization, a problem defined as follows: given a pure Horn CNF, construct a logically equivalent pure Horn CNF which is the shortest possible (either w.r.t. the number of clauses or w.r.t. the total number of literals). Both presented examples give alternative proofs of known complexity results for pure Horn minimization.