License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.CSL.2023.25
URN: urn:nbn:de:0030-drops-174867
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2023/17486/
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Hella, Lauri

The Expressive Power of CSP-Quantifiers

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LIPIcs-CSL-2023-25.pdf (0.8 MB)

Abstract

A generalized quantifier Q_? is called a CSP-quantifier if its defining class ? consists of all structures that can be homomorphically mapped to a fixed finite template structure. For all positive integers n ≥ 2 and k, we define a pebble game that characterizes equivalence of structures with respect to the logic L^k_{∞ω}(CSP^+_n), where CSP^+_n is the union of the class Q₁ of all unary quantifiers and the class CSP_n of all CSP-quantifiers with template structures that have at most n elements. Using these games we prove that for every n ≥ 2 there exists a CSP-quantifier with template of size n+1 which is not definable in L^ω_{∞ω}(CSP^+_n). The proof of this result is based on a new variation of the well-known Cai-Fürer-Immerman construction.

BibTeX - Entry

@InProceedings{hella:LIPIcs.CSL.2023.25,
  author =	{Hella, Lauri},
  title =	{{The Expressive Power of CSP-Quantifiers}},
  booktitle =	{31st EACSL Annual Conference on Computer Science Logic (CSL 2023)},
  pages =	{25:1--25:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-264-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{252},
  editor =	{Klin, Bartek and Pimentel, Elaine},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2023/17486},
  URN =		{urn:nbn:de:0030-drops-174867},
  doi =		{10.4230/LIPIcs.CSL.2023.25},
  annote =	{Keywords: generalized quantifiers, constraint satisfaction problems, pebble games, finite variable logics, descriptive complexity theory}
}

Keywords: generalized quantifiers, constraint satisfaction problems, pebble games, finite variable logics, descriptive complexity theory
Collection: 31st EACSL Annual Conference on Computer Science Logic (CSL 2023)
Issue Date: 2023
Date of publication: 01.02.2023

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