Modulo-counting first-order logic on bounded expansion classes
The result's identifiers
Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F24%3A10493130" target="_blank" >RIV/00216208:11320/24:10493130 - isvavai.cz</a>
Result on the web
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mb_YEFUzo-" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=Mb_YEFUzo-</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1016/j.disc.2023.113700" target="_blank" >10.1016/j.disc.2023.113700</a>
Alternative languages
Result language
angličtina
Original language name
Modulo-counting first-order logic on bounded expansion classes
Original language description
We prove that, on bounded expansion classes, every first-order formula with modulo counting is equivalent, in a linear-time computable monadic expansion, to an existential first-order formula. As a consequence, we derive, on bounded expansion classes, that first-order transductions with modulo counting have the same encoding power as existential first-order transductions. Also, modulo-counting first-order model checking and computation of the size of sets definable in modulo-counting first-order logic can be achieved in linear time on bounded expansion classes. As an application, we prove that a class has structurally bounded expansion if and only if it is a class of bounded depth vertex-minors of graphs in a bounded expansion class. We also show how our results can be used to implement fast matrix calculus on bounded expansion matrices over a finite field.
Czech name
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Czech description
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Classification
Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
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OECD FORD branch
10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)
Result continuities
Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace
Others
Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Discrete Mathematics
ISSN
0012-365X
e-ISSN
1872-681X
Volume of the periodical
347
Issue of the periodical within the volume
8
Country of publishing house
NL - THE KINGDOM OF THE NETHERLANDS
Number of pages
12
Pages from-to
113700
UT code for WoS article
001252004400001
EID of the result in the Scopus database
2-s2.0-85171661362