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
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)
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
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
SIGACT news complexity theory column 43
ACM SIGACT News
Some Dichotomy Theorems for Neural Learning Problems
The Journal of Machine Learning Research
Filter-based resolution principle for lattice-valued propositional logic LP(X)
Information Sciences: an International Journal
On the counting complexity of propositional circumscription
Information Processing Letters
An upper bound on computing all X-minimal models
AI Communications
Non-uniform Boolean Constraint Satisfaction Problems with Cardinality Constraint
CSL '08 Proceedings of the 22nd international workshop on Computer Science Logic
Boolean Constraint Satisfaction Problems: When Does Post's Lattice Help?
Complexity of Constraints
The Complexity of Circumscriptive Inference in Post's Lattice
LPNMR '09 Proceedings of the 10th International Conference on Logic Programming and Nonmonotonic Reasoning
On the boolean connectivity problem for horn relations
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Nonuniform Boolean constraint satisfaction problems with cardinality constraint
ACM Transactions on Computational Logic (TOCL)
On the Boolean connectivity problem for Horn relations
Discrete Applied Mathematics
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
On the hardness of losing weight
ACM Transactions on Algorithms (TALG)
On the tractability of minimal model computation for some CNF theories
Artificial Intelligence
Hi-index | 0.00 |
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 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. We settle this question affirmatively by establishing a dichotomy theorem for the class of all MIN SAT(S)-problems, where S is a finite set of generalized connectives. We also prove a dichotomy theorem for a variant of MIN SAT(S) in which the minimization is restricted to a subset of the variables, whereas the remaining variables may vary arbitrarily (this variant is related to extensions of propositional circumscription and was first studied by Cadoli). Moreover, we show that similar dichotomy theorems hold also when some of the variables are assigned constant values. Finally, we give simple criteria that tell apart the polynomial-time solvable cases of these minimal satisfiability problems from the NP-complete ones.