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On Polynomial-Time Decidability of k-Negations Fragments of FO Theories (Extended Abstract)

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Abstract

This paper introduces a generic framework that provides sufficient conditions for guaranteeing polynomial-time decidability of fixed-negation fragments of first-order theories that adhere to certain fixed-parameter tractability requirements. It enables deciding sentences of such theories with arbitrary existential quantification, conjunction and a fixed number of negation symbols in polynomial time. It was recently shown by Nguyen and Pak [SIAM J. Comput. 51(2): 1-31 (2022)] that an even more restricted such fragment of Presburger arithmetic (the first-order theory of the integers with addition and order) is NP-hard. In contrast, by application of our framework, we show that the fixed negation fragment of weak Presburger arithmetic, which drops the order relation from Presburger arithmetic in favour of equality, is decidable in polynomial time.

BibTeX - Entry

@InProceedings{haase_et_al:LIPIcs.MFCS.2023.52,
  author =	{Haase, Christoph and Mansutti, Alessio and Pouly, Amaury},
  title =	{{On Polynomial-Time Decidability of k-Negations Fragments of FO Theories (Extended Abstract)}},
  booktitle =	{48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)},
  pages =	{52:1--52:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-292-1},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{272},
  editor =	{Leroux, J\'{e}r\^{o}me and Lombardy, Sylvain and Peleg, David},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/18586},
  URN =		{urn:nbn:de:0030-drops-185869},
  doi =		{10.4230/LIPIcs.MFCS.2023.52},
  annote =	{Keywords: first-order theories, arithmetic theories, fixed-parameter tractability}
}

Keywords: first-order theories, arithmetic theories, fixed-parameter tractability
Seminar: 48th International Symposium on Mathematical Foundations of Computer Science (MFCS 2023)
Issue date: 2023
Date of publication: 21.08.2023


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