A universal-algebraic proof of the complexity dichotomy for Monotone Monadic SNP

Publikationstyp
Conference Paper
Date Issued
2018-07
Sprache
English
Author(s)
Bodirsky, Manuel  
Madelaine, Florent  
Mottet, Antoine  
TORE-URI
http://hdl.handle.net/11420/12090
Start Page
105
End Page
114
Citation
33rd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS 2018)
Contribution to Conference
33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018  
Publisher DOI
10.1145/3209108.3209156
Scopus ID
2-s2.0-85051143797
The logic MMSNP is a restricted fragment of existential second-order logic which allows to express many interesting queries in graph theory and finite model theory. The logic was introduced by Feder and Vardi who showed that every MMSNP sentence is computationally equivalent to a finite-domain constraint satisfaction problem (CSP); the involved probabilistic reductions were derandomized by Kun using explicit constructions of expander structures. We present a new proof of the reduction to finite-domain CSPs that does not rely on the results of Kun. This new proof allows us to obtain a stronger statement and to verify the Bodirsky-Pinsker dichotomy conjecture for CSPs in MMSNP. Our approach uses the fact that every MMSNP sentence describes a finite union of CSPs for countably infinite -categorical structures; moreover, by a recent result of Hubika and Neetil, these structures can be expanded to homogeneous structures with finite relational signature and the Ramsey property. This allows us to use the universal-algebraic approach to study the computational complexity of MMSNP.