Combinatorica
The alternating fixpoint of logic programs with negation
PODS '89 Proceedings of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
Journal of the ACM (JACM)
The well-founded semantics for general logic programs
Journal of the ACM (JACM)
On the relations between stable and well-founded semantics of logic programs
Theoretical Computer Science - Selected papers of the Second International Conference on algebraic and logic programming, Nancy, France, October 1–3, 1990
The alternating fixpoint of logic programs with negation
PODS '89 Selected papers of the eighth ACM SIGACT-SIGMOD-SIGART symposium on Principles of database systems
A Computing Procedure for Quantification Theory
Journal of the ACM (JACM)
WFS + Branch and Bound = Stable Models
IEEE Transactions on Knowledge and Data Engineering
Computation of Stable Models and Its Integration with Logical Query Processing
IEEE Transactions on Knowledge and Data Engineering
EVIDENCE FOR A SATISFIABILITY THRESHOLD FOR RANDOM 3CNF FORMULAS
EVIDENCE FOR A SATISFIABILITY THRESHOLD FOR RANDOM 3CNF FORMULAS
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We empirically investigated the difficulty of finding stable models for logic programs using backtracking, by trying to identify what makes random instances easy or hard. Additionally, we empirically investigated the effectiveness of the 4‐valued Kripke–Kleene semantics (4KK) and the 4‐valued well‐founded semantics (4WF) in the Niemelä and Simons’ backtracking algorithm, smodels, for finding stable models. We studied the behavior of 4KK and 4WF in a parameterized distribution of random propositional logic programs of fixed rule‐length k. In all of our experiments, 4KK and 4WF (both modified to extend an input partial truth assignment) were computed with respect to a fixed percentage of proposition letters (randomly chosen) initially assigned TRUE and a fixed percentage (randomly chosen) initially assigned FALSE. There exists a region, R, in the parameter space of our distribution where smodels required a large number of recursive calls to determine if programs generated in this region have any stable models. Hence, the “hardest” programs for smodels to determine if a stable model exists lie in R. Additionally, there exists a subregion of R where smodels made significantly fewer recursive calls when using 4WF as a pruning technique than when using 4KK. To gain a deeper insight into the causes for the “hardness” of programs in R and the differences between 4WF and 4KK as pruning techniques in smodels, we examined more closely the behavior of 4KK and 4WF. There exists a region in which a very small percentage of inconsistent models were produced by both 4KK and 4WF, thereby providing very little information useful for smodels to immediately backtrack. This region roughly corresponded to the above region where smodels required a large number of recursive calls. Also, there exists a region in which both 4KK and 4WF produced a high percentage of inconsistent models, thereby providing information useful for smodels to immediately backtrack.