ON GUARDED EXTENSIONS OF MMSNP

Result code in IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216208%3A11320%2F25%3A10509762" target="_blank" >RIV/00216208:11320/25:10509762 - isvavai.cz</a>

Result on the web

<a href="https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fo7tmCNxY3" target="_blank" >https://verso.is.cuni.cz/pub/verso.fpl?fname=obd_publikace_handle&handle=fo7tmCNxY3</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.46298/LMCS-21(4:15)2025" target="_blank" >10.46298/LMCS-21(4:15)2025</a>

Result language

angličtina

Original language name

ON GUARDED EXTENSIONS OF MMSNP

Original language description

. Feder and Vardi showed that the class Monotone Monadic SNP without inequality (MMSNP) has a P vs NP-complete dichotomy if and only if such a dichotomy holds for finite-domain Constraint Satisfaction Problems (CSPs). Moreover, they showed that none of the three classes obtained by removing one of the defining properties of MMSNP (monotonicity, monadicity, no inequality) has a dichotomy. The overall objective of this paper is to study the gaps between MMSNP and each of these three superclasses, where the existence of a dichotomy remains unknown. For the gap between MMSNP and Monotone SNP without inequality, we study the class Guarded Monotone SNP without inequality (GMSNP) introduced by Bienvenu, ten Cate, Lutz, and Wolter, and prove that GMSNP has a dichotomy if and only if a dichotomy holds for GMSNP problems over signatures consisting of a unique relation symbol. For the gap between MMSNP and MMSNP with inequality, we introduce a new class MMSNP with guarded inequality, that lies between MMSNP and MMSNP with inequality and that is strictly more expressive than the former and still has a dichotomy. For the gap between MMSNP and Monadic SNP without inequality, we introduce a logic that extends the class of Matrix Partitions in a similar way how MMSNP extends finite-domain CSP, and pose an open question about the existence of a dichotomy for this class. Finally, we revisit the theorem of Feder and Vardi, which claims that the class NP embeds into MMSNP with inequality. We give a detailed proof of this theorem as it ensures no dichotomy for the right-hand side class of each of the three gaps.

Czech name

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Czech description

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Type

J_imp - 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

Project

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Continuities

I - Institucionalni podpora na dlouhodoby koncepcni rozvoj vyzkumne organizace

Publication year

2025

Confidentiality

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

Name of the periodical

Logical Methods in Computer Science

ISSN

1860-5974

e-ISSN

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Volume of the periodical

21

Issue of the periodical within the volume

4

Country of publishing house

DE - GERMANY

Number of pages

31

Pages from-to

15

UT code for WoS article

001608196800001

EID of the result in the Scopus database

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