The Expressive Power of CSP-Quantifiers

Author Lauri Hella

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Lauri Hella
  • Faculty of Information Technology and Communication Sciences, Tampere University, Finland

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Lauri Hella. The Expressive Power of CSP-Quantifiers. In 31st EACSL Annual Conference on Computer Science Logic (CSL 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 252, pp. 25:1-25:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)


A generalized quantifier Q_𝒦 is called a CSP-quantifier if its defining class 𝒦 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.

Subject Classification

ACM Subject Classification
  • Theory of computation → Finite Model Theory
  • generalized quantifiers
  • constraint satisfaction problems
  • pebble games
  • finite variable logics
  • descriptive complexity theory


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