SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS
The result's identifiers
Result code in 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>
Result on the web
<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>
Alternative languages
Result language
angličtina
Original language name
SMALL PROMISE CSPS THAT REDUCE TO LARGE CSPS
Original language description
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].
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
10101 - Pure mathematics
Result continuities
Project
Result was created during the realization of more than one project. More information in the Projects tab.
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)
Others
Publication year
2022
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů
Data specific for result type
Name of the periodical
Logical Methods in Computer Science
ISSN
1860-5974
e-ISSN
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Volume of the periodical
18
Issue of the periodical within the volume
3
Country of publishing house
DE - GERMANY
Number of pages
14
Pages from-to
25
UT code for WoS article
000844642700001
EID of the result in the Scopus database
2-s2.0-85137767941