Extended Horn sets in propositional logic
Journal of the ACM (JACM)
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
A Complexity Index for Satisfiability Problems
SIAM Journal on Computing
Horn approximations of empirical data
Artificial Intelligence
A dichotomy theorem for maximum generalized satisfiability problems
Journal of Computer and System Sciences - Special issue on selected papers presented at the 24th annual ACM symposium on the theory of computing (STOC '92)
Complexity of generalized satisfiability counting problems
Information and Computation
Artificial Intelligence
On the complexity of dualization of monotone disjunctive normal forms
Journal of Algorithms
Defaults and relevance in model-based reasoning
Artificial Intelligence - Special issue on relevance
The Inverse Satisfiability Problem
SIAM Journal on Computing
Computing intersections of horn theories for reasoning with models
Artificial Intelligence
Renaming a Set of Clauses as a Horn Set
Journal of the ACM (JACM)
On connected Boolean functions
Discrete Applied Mathematics - Special issue on the satisfiability problem and Boolean functions
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Approximability of Constraint Satisfaction Problems
SIAM Journal on Computing
A Dichotomy Theorem for Constraints on a Three-Element Set
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
On Horn Envelopes and Hypergraph Transversals
ISAAC '93 Proceedings of the 4th International Symposium on Algorithms and Computation
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
The complexity of minimal satisfiability problems
Information and Computation
On the solution-space geometry of random constraint satisfaction problems
Proceedings of the thirty-eighth annual ACM symposium on Theory of computing
A Complete Classification of the Complexity of Propositional Abduction
SIAM Journal on Computing
Translating between Horn representations and their characteristic models
Journal of Artificial Intelligence Research
The connectivity of boolean satisfiability: computational and structural dichotomies
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
An exact algorithm for the boolean connectivity problem for k-CNF
SAT'10 Proceedings of the 13th international conference on Theory and Applications of Satisfiability Testing
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Gopalan et al. studied in ICALP06 [17] connectivity properties of the solution-space of Boolean formulas, and investigated complexity issues on the connectivity problems in Schaefer's framework. A set S of logical relations is Schaefer if all relations in S are either bijunctive, Horn, dual Horn, or affine. They conjectured that the connectivity problem for Schaefer is in P. We disprove their conjecture by showing that there exists a set S of Horn relations such that the connectivity problem for S is coNP-complete. We also show that the connectivity problem for bijunctive relations can be solved in O(min{n|φ|, T(n)}) time, where n denotes the number of variables, φ denotes the corresponding 2-CNF formula, and T(n) denotes the time needed to compute the transitive closure of a directed graph of n vertices. Furthermore, we investigate a tractable aspect of Horn and dual Horn relations with respect to characteristic sets.