Design by exmple: An application of Armstrong relations
Journal of Computer and System Sciences
A theory of diagnosis from first principles
Artificial Intelligence
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
Learning Conjunctions of Horn Clauses
Machine Learning - Computational learning theory
AAAI'94 Proceedings of the twelfth national conference on Artificial intelligence (vol. 2)
Horn approximations of empirical data
Artificial Intelligence
On the Learnability of Disjunctive Normal Form Formulas
Machine Learning
Approximate inference of functional dependencies from relations
ICDT '92 Selected papers of the fourth international conference on Database theory
Identifying the Minimal Transversals of a Hypergraph and Related Problems
SIAM Journal on Computing
Complexity of identification and dualization of positive Boolean functions
Information and Computation
On the Structure of Armstrong Relations for Functional Dependencies
Journal of the ACM (JACM)
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
Exact learning via the Monotone theory
SFCS '93 Proceedings of the 1993 IEEE 34th Annual Foundations of Computer Science
IJCAI'95 Proceedings of the 14th international joint conference on Artificial intelligence - Volume 1
Data mining, hypergraph transversals, and machine learning (extended abstract)
PODS '97 Proceedings of the sixteenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Generating all maximal independent sets of bounded-degree hypergraphs
COLT '97 Proceedings of the tenth annual conference on Computational learning theory
Computing intersections of Horn theories for reasoning with models
AAAI '98/IAAI '98 Proceedings of the fifteenth national/tenth conference on Artificial intelligence/Innovative applications of artificial intelligence
On functional dependencies in q-Horn theories
Artificial Intelligence
New results on monotone dualization and generating hypergraph transversals
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Translation among CNFs, characteristic models and ordered binary decision diagrams
Information Processing Letters
Approximation of Relations by Propositional Formulas: Complexity and Semantics
Proceedings of the 5th International Symposium on Abstraction, Reformulation and Approximation
Hypergraph Transversal Computation and Related Problems in Logic and AI
JELIA '02 Proceedings of the European Conference on Logics in Artificial Intelligence
Translation among CNFs, Characteristic Models and Ordered Binary Decision Diagrams
ISAAC '01 Proceedings of the 12th International Symposium on Algorithms and Computation
Discovering all most specific sentences
ACM Transactions on Database Systems (TODS)
First order LUB approximations: characterization and algorithms
Artificial Intelligence - Special volume on reformulation
On computing all abductive explanations from a propositional Horn theory
Journal of the ACM (JACM)
Computational aspects of monotone dualization: A brief survey
Discrete Applied Mathematics
First order LUB approximations: characterization and algorithms
Artificial Intelligence - Special volume on reformulation
On the boolean connectivity problem for horn relations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Boolean approximation revisited
SARA'07 Proceedings of the 7th International conference on Abstraction, reformulation, and approximation
About keys of formal context and conformal hypergraph
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
On the merge of factor canonical bases
ICFCA'08 Proceedings of the 6th international conference on Formal concept analysis
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
Computing premises of a minimal cover of functional dependencies is intractable
Discrete Applied Mathematics
Horn clause contraction functions
Journal of Artificial Intelligence Research
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Characteristic models are an alternative, model based, representation for Horn expressions. It has been shown that these two representations are incomparable and each has its advantages over the other. It is therefore natural to ask what is the cost of translating, back and forth, between these representations. Interestingly, the same translation questions arise in database theory, where it has applications to the design of relational databases. This paper studies the computational complexity of these problems. Our main result is that the two translation problems are equivalent under polynomial reductions, and that they are equivalent to the corresponding decision problem. Namely, translating is equivalent to deciding whether a given set of models is the set of characteristic models for a given Horn expression. We also relate these problems to the hypergraph transversal problem, a well known problem which is related to other applications in AI and for which no polynomial time algorithm is known. It is shown that in general our translation problems are at least as hard as the hypergraph transversal problem, and in a special case they are equivalent to it.