## Authors: Manuel Bodirsky, Florent Madelaine and Antoine Mottet

## Paper Information

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

Authors: | Manuel Bodirsky, Florent Madelaine and Antoine Mottet |

Proceedings: | LICS PDF files |

Editors: | Anuj Dawar and Erich Grädel |

Keywords: | MMSNP, constraint satisfaction problems, universal algebra, model theory, Ramsey theory, finite model theory, complexity dichotomy, polynomial-time tractability |

Abstract: | ABSTRACT. 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 which does not rely on the results of Kun. Our approach uses the fact that every MMSNP sentence describes a finite union of CSPs for countably infinite ω-categorical structures; moreover, by a recent result of Hubicka and Nesetril, 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. In particular, we verify the more general Bodirsky-Pinsker dichotomy conjecture for CSPs in MMSNP. |

Pages: | 10 |

Talk: | Jul 11 11:20 (Session 64D) |

Paper: |