@misc{GebserHarrisonKaminskietal.2015,
  author    = {Gebser, Martin and Harrison, Amelia and Kaminski, Roland and Lifschitz, Vladimir and Schaub, Torsten H.},
  title     = {Abstract gringo},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {592},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41475},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-414751},
  pages     = {15},
  year      = {2015},
  abstract  = {This paper defines the syntax and semantics of the input language of the ASP grounder gringo. The definition covers several constructs that were not discussed in earlier work on the semantics of that language, including intervals, pools, division of integers, aggregates with non-numeric values, and lparse-style aggregate expressions. The definition is abstract in the sense that it disregards some details related to representing programs by strings of ASCII characters. It serves as a specification for gringo from Version 4.5 on.},
  language  = {en}
}
@misc{GebserLeeLierler2011,
  author    = {Gebser, Martin and Lee, Joohyung and Lierler, Yuliya},
  title     = {On elementary loops of logic programs},
  series = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  journal   = {Postprints der Universit{\"a}t Potsdam : Mathematisch-Naturwissenschaftliche Reihe},
  number    = {566},
  issn      = {1866-8372},
  doi       = {10.25932/publishup-41309},
  url       = {http://nbn-resolving.de/urn:nbn:de:kobv:517-opus4-413091},
  pages     = {36},
  year      = {2011},
  abstract  = {Using the notion of an elementary loop, Gebser and Schaub (2005. Proceedings of the Eighth International Conference on Logic Programming and Nonmonotonic Reasoning (LPNMR'05 ), 53-65) refined the theorem on loop formulas attributable to Lin and Zhao (2004) by considering loop formulas of elementary loops only. In this paper, we reformulate the definition of an elementary loop, extend it to disjunctive programs, and study several properties of elementary loops, including how maximal elementary loops are related to minimal unfounded sets. The results provide useful insights into the stable model semantics in terms of elementary loops. For a nondisjunctive program, using a graph-theoretic characterization of an elementary loop, we show that the problem of recognizing an elementary loop is tractable. On the other hand, we also show that the corresponding problem is coNP-complete for a disjunctive program. Based on the notion of an elementary loop, we present the class of Head-Elementary-loop-Free (HEF) programs, which strictly generalizes the class of Head-Cycle-Free (HCF) programs attributable to Ben-Eliyahu and Dechter (1994. Annals of Mathematics and Artificial Intelligence 12, 53-87). Like an HCF program, an HEF program can be turned into an equivalent nondisjunctive program in polynomial time by shifting head atoms into the body.},
  language  = {en}
}