eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-02-01
25:1
25:19
10.4230/LIPIcs.CSL.2023.25
article
The Expressive Power of CSP-Quantifiers
Hella, Lauri
1
https://orcid.org/0000-0002-9117-8124
Faculty of Information Technology and Communication Sciences, Tampere University, Finland
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol252-csl2023/LIPIcs.CSL.2023.25/LIPIcs.CSL.2023.25.pdf
generalized quantifiers
constraint satisfaction problems
pebble games
finite variable logics
descriptive complexity theory