On the problem of computing the well-founded semantics

Zbigniew Lonc, Mirosław Truszczyński

Research output: Contribution to journalArticlepeer-review

5 Scopus citations


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)\ x 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.

Original languageEnglish
Pages (from-to)591-609
Number of pages19
JournalTheory and Practice of Logic Programming
Issue number5
StatePublished - Sep 2001


  • Alternating fixpoint
  • Well-founded semantics

ASJC Scopus subject areas

  • Software
  • Theoretical Computer Science
  • Hardware and Architecture
  • Computational Theory and Mathematics
  • Artificial Intelligence


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