The complexity of propositional closed world reasoning and circumscription
Journal of Computer and System Sciences
New methods for 3-SAT decision and worst-case analysis
Theoretical Computer Science
Declarative problem-solving in DLV
Logic-based artificial intelligence
Nonmonotonic Logic: Context-Dependent Reasoning
Nonmonotonic Logic: Context-Dependent Reasoning
Extending and implementing the stable model semantics
Artificial Intelligence
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Logic programs with stable model semantics as a constraint programming paradigm
Annals of Mathematics and Artificial Intelligence
A deterministic (2 - 2/(k+ 1))n algorithm for k-SAT based on local search
Theoretical Computer Science
A Tableau Calculus for Minimal Model Reasoning
TABLEAUX '96 Proceedings of the 5th International Workshop on Theorem Proving with Analytic Tableaux and Related Methods
Computing stable models: worst-case performance estimates
Theory and Practice of Logic Programming
Predicate-calculus-based logics for modeling and solving search problems
ACM Transactions on Computational Logic (TOCL)
Quo Vadis Answer Set Programming?
ICLP '08 Proceedings of the 24th International Conference on Logic Programming
Counting independent sets in claw-free graphs
WG'11 Proceedings of the 37th international conference on Graph-Theoretic Concepts in Computer Science
Counting maximal independent sets in subcubic graphs
SOFSEM'12 Proceedings of the 38th international conference on Current Trends in Theory and Practice of Computer Science
On the tractability of minimal model computation for some CNF theories
Artificial Intelligence
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We propose and study algorithms to compute minimal models, stable models and answer sets of $t$-CNF theories, and normal and disjunctive $t$-programs. We are especially interested in algorithms with non-trivial worst-case performance bounds. The bulk of the paper is concerned with the classes of 2- and 3-CNF theories, and normal and disjunctive 2- and 3-programs, for which we obtain significantly stronger results than those implied by our general considerations. We show that one can find all minimal models of 2-CNF theories and all answer sets of disjunctive 2-programs in time $O(m1\mbox{.}4422\mbox{..}^n)$. Our main results concern computing stable models of normal 3-programs, minimal models of 3-CNF theories and answer sets of disjunctive 3-programs. We design algorithms that run in time $O(m1\mbox{.}6701\mbox{..}^n)$, in the case of the first problem, and in time $O(mn^2 2\mbox{.}2782\mbox{..}^n)$, in the case of the latter two. All these bounds improve by exponential factors the best algorithms known previously. We also obtain closely related upper bounds on the number of minimal models, stable models and answer sets a $t$-CNF theory, a normal $t$-program or a disjunctive $t$-program may have.