Structural Properties of the First-Order Transduction Quasiorder

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

Structural Properties of the First-Order Transduction Quasiorder

Popis výsledku v původním jazyce

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 &gt;= 1 form a strict hierarchy in the FO transduction quasiorder.

Název v anglickém jazyce

Structural Properties of the First-Order Transduction Quasiorder

Popis výsledku anglicky

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 &gt;= 1 form a strict hierarchy in the FO transduction quasiorder.

Druh

D - Stať ve sborníku

CEP obor

—

OECD FORD obor

10201 - Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8)

Projekt

—

Návaznosti

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Rok uplatnění

2022

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název statě ve sborníku

Leibniz International Proceedings in Informatics, LIPIcs

ISBN

978-3-95977-218-1

ISSN

1868-8969

e-ISSN

—

Počet stran výsledku

16

Strana od-do

—

Název nakladatele

Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing

Místo vydání

Dagstuhl, Německo

Místo konání akce

Göttingen, Německo

Datum konání akce

14. 2. 2022

Typ akce podle státní příslušnosti

WRD - Celosvětová akce

Kód UT WoS článku

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