## Abstract

We study the problem of conjunctive query evaluation relative to a class of queries; this problem is formulated here as the relational homomorphism problem relative to a class of structures A, wherein each instance must be a pair of structures such that the first structure is an element of A. We present a comprehensive complexity classification of these problems, which strongly links graph-theoretic properties of A to the complexity of the corresponding homomorphism problem. In particular, we define a binary relation on graph classes and completely describe the resulting hierarchy given by this relation. This binary relation is defined in terms of a notion which we call graph deconstruction and which is a variant of the well-known notion of tree decomposition. We then use this hierarchy of graph classes to infer a complexity hierarchy of homomorphism problems which is comprehensive up to a computationally very weak notion of reduction, namely, a parameterized version of quantifier-free reductions. In doing so, we obtain a significantly refined complexity classification of homomorphism problems, as well as a unifying, modular, and conceptually clean treatment of existing complexity classifications. We then present and develop the theory of Ehrenfeucht- Fraïssé-style pebble games which solve the homomorphism problems where the cores of the structures in A have bounded tree depth. Finally, we use our framework to classify the complexity of model checking existential sentences having bounded quantifier rank.

Originalsprache | Englisch |
---|---|

Titel | Proceedings of the Joint Meeting of the 23rd EACSL Annual Conference on Computer Science Logic, CSL 2014 and the 29th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2014 |

Untertitel | Vienna, Austria — July 14 - 18, 2014 |

Herausgeber (Verlag) | Association for Computing Machinery (ACM) |

ISBN (Print) | 9781450328869 |

DOIs | |

Publikationsstatus | Veröffentlicht - 2014 |

## ÖFOS 2012

- 102031 Theoretische Informatik
- 101013 Mathematische Logik
- 101011 Graphentheorie