Minimal representation of directed hypergraphs
SIAM Journal on Computing
Information Processing Letters
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
Optimal compression of propositional Horn knowledge bases: complexity and approximation
Artificial Intelligence
The algorithmic aspects of the regularity lemma
Journal of Algorithms
Matters horn and other features in the computational learning theory landscape: the notion of membership
Approximating the minimum strongly connected subgraph via a matching lower bound
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Propositional Logic: Deduction and Algorithms
Propositional Logic: Deduction and Algorithms
The minimum equivalent DNF problem and shortest implicants
Journal of Computer and System Sciences
Quasi-Acyclic Propositional Horn Knowledge Bases: Optimal Compression
IEEE Transactions on Knowledge and Data Engineering
Open Mind Common Sense: Knowledge Acquisition from the General Public
On the Move to Meaningful Internet Systems, 2002 - DOA/CoopIS/ODBASE 2002 Confederated International Conferences DOA, CoopIS and ODBASE 2002
Artificial Intelligence: A Modern Approach
Artificial Intelligence: A Modern Approach
Discrete Applied Mathematics - Special issue: The 1998 conference on ordinal and symbolic data analysis (OSDA '98)
Hardness of Approximating Minimization Problems
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
Feasibly constructive proofs and the propositional calculus (Preliminary Version)
STOC '75 Proceedings of seventh annual ACM symposium on Theory of computing
Hardness of Approximation for Vertex-Connectivity Network Design Problems
SIAM Journal on Computing
Theory of Relational Databases
Theory of Relational Databases
Approximating Transitive Reductions for Directed Networks
WADS '09 Proceedings of the 11th International Symposium on Algorithms and Data Structures
Combinatorial Problems for Horn Clauses
Graph Theory, Computational Intelligence and Thought
Horn complements: towards horn-to-horn belief revision
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 1
On the gap between ess(f) and cnf_size(f)
Discrete Applied Mathematics
Hydras: directed hypergraphs and horn formulas
WG'12 Proceedings of the 38th international conference on Graph-Theoretic Concepts in Computer Science
A decomposition method for CNF minimality proofs
Theoretical Computer Science
| Hi-index | 0.00 |
The minimization problem for Horn formulas is to find a Horn formula equivalent to a given Horn formula, using a minimum number of clauses. A 2log1-ε(n)-inapproximability result is proven, which is the first inapproximability result for this problem. We also consider several other versions of Horn minimization. The more general version which allows for the introduction of new variables is known to be too difficult as its equivalence problem is co-NP-complete. Therefore, we propose a variant called Steiner-minimization, which allows for the introduction of new variables in a restricted manner. Steiner-minimization of Horn formulas is shown to be MAX-SNP-hard. In the positive direction, a o(n), namely, O(n log log n/(log n)1/4)-approximation algorithm is given for the Steiner-minimization of definite Horn formulas. The algorithm is based on a new result in algorithmic extremal graph theory, on partitioning bipartite graphs into complete bipartite graphs, which may be of independent interest. Inapproximability results and approximation algorithms are also given for restricted versions of Horn minimization, where only clauses present in the original formula may be used.