Structural Properties of the First-Order Transduction Quasiorder

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10454278" target="_blank" >RIV/00216208:11320/22:10454278 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.4230/LIPIcs.CSL.2022.31" target="_blank" >https://doi.org/10.4230/LIPIcs.CSL.2022.31</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.4230/LIPIcs.CSL.2022.31" target="_blank" >10.4230/LIPIcs.CSL.2022.31</a>

Result language
angličtina
Original language name
Structural Properties of the First-Order Transduction Quasiorder
Original language description
Logical transductions provide a very useful tool to encode classes of structures inside other classes of structures. In this paper we study first-order (FO) transductions and the quasiorder they induce on infinite classes of finite graphs. Surprisingly, this quasiorder is very complex, though shaped by the locality properties of first-order logic. This contrasts with the conjectured simplicity of the monadic second order (MSO) transduction quasiorder. We first establish a local normal form for FO transductions, which is of independent interest. Then we prove that the quotient partial order is a bounded distributive join-semilattice, and that the subposet of additive classes is also a bounded distributive join-semilattice. The FO transduction quasiorder has a great expressive power, and many well studied class properties can be defined using it. We apply these structural properties to prove, among other results, that FO transductions of the class of paths are exactly perturbations of classes with bounded bandwidth, that the local variants of monadic stability and monadic dependence are equivalent to their (standard) non-local versions, and that the classes with pathwidth at most k, for k >= 1 form a strict hierarchy in the FO transduction quasiorder.
Czech name
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Czech description
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Type
D - Article in proceedings
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)

Project
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Continuities
I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Article name in the collection
Leibniz International Proceedings in Informatics, LIPIcs
ISBN
978-3-95977-218-1
ISSN
1868-8969
e-ISSN
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Number of pages
16
Pages from-to
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Publisher name
Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Place of publication
Dagstuhl, Německo
Event location
Göttingen, Německo
Event date
Feb 14, 2022
Type of event by nationality
WRD - Celosvětová akce
UT code for WoS article
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