SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS
Identifikátory výsledku
Kód výsledku v IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F22%3A10454319" target="_blank" >RIV/00216208:11320/22:10454319 - isvavai.cz</a>
Výsledek na webu
<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eZY3b.xnnX" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=eZY3b.xnnX</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.46298/LMCS-18(3:25)2022" target="_blank" >10.46298/LMCS-18(3:25)2022</a>
Alternativní jazyky
Jazyk výsledku
angličtina
Název v původním jazyce
SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS
Popis výsledku v původním jazyce
For relational structures A, B of the same signature, the Promise Constraint Satisfaction Problem PCSP(A, B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases. If there exists a structure C with homomorphisms A -> C -> B, then PCSP(A, B) reduces naturally to CSP(C). To the best of our knowledge all known tractable PCSPs reduce to tractable CSPs in this way. However Barto [Bar19] showed that some PCSPs over finite structures A, B require solving CSPs over infinite C. We show that even when such a reduction to some finite C is possible, this structure may become arbitrarily large. For every integer n > 1 and every prime p we give A, B of size n with a single relation of arity n(p) such that PCSP(A, B) reduces via a chain of homomorphisms A -> C -> B to a tractable CSP over some C of size p but not over any smaller structure. In a second family of examples, for every prime p >= 7 we construct A, B of size p - 1 with a single ternary relation such that PCSP(A, B) reduces via A -> C -> B to a tractable CSP over some C of size p but not over any smaller structure. In contrast we show that if A, B are graphs and PCSP(A, B) reduces to a tractable CSP(C) for some finite digraph C, then already A or B has a tractable CSP. This extends results and answers a question of [DSM(+)21].
Název v anglickém jazyce
SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS
Popis výsledku anglicky
For relational structures A, B of the same signature, the Promise Constraint Satisfaction Problem PCSP(A, B) asks whether a given input structure maps homomorphically to A or does not even map to B. We are promised that the input satisfies exactly one of these two cases. If there exists a structure C with homomorphisms A -> C -> B, then PCSP(A, B) reduces naturally to CSP(C). To the best of our knowledge all known tractable PCSPs reduce to tractable CSPs in this way. However Barto [Bar19] showed that some PCSPs over finite structures A, B require solving CSPs over infinite C. We show that even when such a reduction to some finite C is possible, this structure may become arbitrarily large. For every integer n > 1 and every prime p we give A, B of size n with a single relation of arity n(p) such that PCSP(A, B) reduces via a chain of homomorphisms A -> C -> B to a tractable CSP over some C of size p but not over any smaller structure. In a second family of examples, for every prime p >= 7 we construct A, B of size p - 1 with a single ternary relation such that PCSP(A, B) reduces via A -> C -> B to a tractable CSP over some C of size p but not over any smaller structure. In contrast we show that if A, B are graphs and PCSP(A, B) reduces to a tractable CSP(C) for some finite digraph C, then already A or B has a tractable CSP. This extends results and answers a question of [DSM(+)21].
Klasifikace
Druh
J<sub>imp</sub> - Článek v periodiku v databázi Web of Science
CEP obor
—
OECD FORD obor
10101 - Pure mathematics
Návaznosti výsledku
Projekt
Výsledek vznikl pri realizaci vícero projektů. Více informací v záložce Projekty.
Návaznosti
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Ostatní
Rok uplatnění
2022
Kód důvěrnosti údajů
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Údaje specifické pro druh výsledku
Název periodika
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
—
Svazek periodika
18
Číslo periodika v rámci svazku
3
Stát vydavatele periodika
DE - Spolková republika Německo
Počet stran výsledku
14
Strana od-do
25
Kód UT WoS článku
000844642700001
EID výsledku v databázi Scopus
2-s2.0-85137767941