Applications of circumscription to formalizing common-sense knowledge
Artificial Intelligence
On the complexity of H-coloring
Journal of Combinatorial Theory Series B
Structure identification in relational data
Artificial Intelligence - Special volume on constraint-based reasoning
The complexity of model checking for circumscriptive formulae
Information Processing Letters
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
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
Closure properties of constraints
Journal of the ACM (JACM)
Conjunctive-query containment and constraint satisfaction
PODS '98 Proceedings of the seventeenth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Finding almost-satisfying assignments
STOC '98 Proceedings of the thirtieth annual ACM symposium on Theory of computing
The Inverse Satisfiability Problem
SIAM Journal on Computing
On the Structure of Polynomial Time Reducibility
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
Optimal Satisfiability for Propositional Calculi and Constraint Satisfaction Problems
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Constraint Satisfaction: The Approximability of Minimization Problems
CCC '97 Proceedings of the 12th Annual IEEE Conference on Computational Complexity
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Looking for a Version of Schaefer''s Dichotomy Theorem When Each Variable Occurs at Most Twice
Looking for a Version of Schaefer''s Dichotomy Theorem When Each Variable Occurs at Most Twice
IJCAI'85 Proceedings of the 9th international joint conference on Artificial intelligence - Volume 1
The Inference Problem for Propositional Circumscription of Affine Formulas Is coNP-Complete
STACS '03 Proceedings of the 20th Annual Symposium on Theoretical Aspects of Computer Science
The Complexity of Constraints on Intervals and Lengths
STACS '02 Proceedings of the 19th Annual Symposium on Theoretical Aspects of Computer Science
Equivalence and Isomorphism for Boolean Constraint Satisfaction
CSL '02 Proceedings of the 16th International Workshop and 11th Annual Conference of the EACSL on Computer Science Logic
Substitutional definition of satisfiability in classical propositional logic
SAT'05 Proceedings of the 8th international conference on Theory and Applications of Satisfiability Testing
MFCS'05 Proceedings of the 30th international conference on Mathematical Foundations of Computer Science
Quantified constraint satisfaction, maximal constraint languages, and symmetric polymorphisms
STACS'05 Proceedings of the 22nd annual conference on Theoretical Aspects of Computer Science
| Hi-index | 0.01 |
A dichotomy theorem for a class of decision problems is a result asserting that certain problems in the class are solvable in polynomial time, while the rest are NP-complete. The first remarkable such dichotomy theorem was proved by T.J. Schaefer in 1978. It concerns the class of generalized satisfiability problems SAT(S), whose input is a CNF(S)-formula, i.e., a formula constructed from elements of a fixed set S of generalized connectives using conjunctions and substitutions by variables. Here, we investigate the complexity of minimal satisfiability problems MIN SAT(S), where S is a fixed set of generalized connectives. The input to such a problem is a CNF(S)-formula and a satisfying truth assignment; the question is to decide whether there is another satisfying truth assignment that is strictly smaller than the given truth assignment with respect to the coordinate-wise partial order on truth assignments. Minimal satisfiability problems were first studied by researchers in artificial intelligence while investigating the computational complexity of propositional circumscription. The question of whether dichotomy theorems can be proved for these problems was raised at that time, but was left open. In this paper, we settle this question affirmatively by establishing a dichotomy theorem for the class of all MIN SAT(S)-problems.