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)
Tabled evaluation with delaying for general logic programs
Journal of the ACM (JACM)
Characterizations of the Disjunctive Well-Founded Semantics: Confluent Calculi and Iterated GCWA
Journal of Automated Reasoning
WFS + Branch and Bound = Stable Models
IEEE Transactions on Knowledge and Data Engineering
Computing Well-founded Semantics Faster
LPNMR '95 Proceedings of the Third International Conference on Logic Programming and Nonmonotonic Reasoning
Improving the Alternating Fixpoint: The Transformation Approach
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
XSB: A System for Effciently Computing WFS
LPNMR '97 Proceedings of the 4th International Conference on Logic Programming and Nonmonotonic Reasoning
Transformation-based bottom-up computation of the well-founded model
Theory and Practice of Logic Programming
Computing stable models: worst-case performance estimates
Theory and Practice of Logic Programming
Graphs and colorings for answer set programming
Theory and Practice of Logic Programming
Well-founded semantics and the algebraic theory of non-monotone inductive definitions
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
Rules and logic programming for the web
RW'11 Proceedings of the 7th international conference on Reasoning web: semantic technologies for the web of data
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The well-founded semantics is one of the most widely studied and used semantics of logic programs with negation. In the case of finite propositional programs, it can be computed in polynomial time, more specifically, in O(∣At(P)∣ × size(P)) steps, where size(P) denotes the total number of occurrences of atoms in a logic program P. This bound is achieved by an algorithm introduced by Van Gelder and known as the alternating-fixpoint algorithm. Improving on the alternating-fixpoint algorithm turned out to be difficult. In this paper we study extensions and modifications of the alternating-fixpoint approach. We then restrict our attention to the class of programs whose rules have no more than one positive occurrence of an atom in their bodies. For programs in that class we propose a new implementation of the alternating-fixpoint method in which false atoms are computed in a top-down fashion. We show that our algorithm is faster than other known algorithms and that for a wide class of programs it is linear and so, asymptotically optimal.