arXiv subjects

Moritz Müller

Publications and source records attributed to Moritz Müller.

23 records · Page 2Linked to original sources

arXiv2016

One Hierarchy Spawns Another: Graph Deconstructions and the Complexity Classification of Conjunctive Queries

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, which is a preorder, and completely describe the resulting hierarchy given by this relation. This 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 first-order reduction. 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-Fraisse-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.

cs.CC↗

arXiv2015

Interfacial charge rearrangement and intermolecular interactions: Density-functional theory study of free-base porphine adsorbed on Ag(111) and Cu(111)

We employ dispersion-corrected density-functional theory to study the adsorption of tetrapyrrole 2H-porphine (2H-P) at Cu(111) and Ag(111). Various contributions to adsorbate-substrate and adsorbate-adsorbate interactions are systematically extracted to analyze the self-assembly behavior of this basic building block to porphyrin-based metal-organic nanostructures. This analysis reveals a surprising importance of substrate-mediated van der Waals interactions between 2H-P molecules, in contrast to negligible direct dispersive interactions. The resulting net repulsive interactions rationalize the experimentally observed tendency for single molecule adsorption.

physics.chem-ph↗

arXiv2014

Topological dynamics of unordered Ramsey structures

In this paper we investigate the connections between Ramsey properties of Fraisse classes K and the universal minimal flow M(G_K) of the automorphism group G_K of their Fraisse limits. As an extension of a result of Kechris, Pestov and Todorcevic we show that if the class K has finite Ramsey degree for embeddings, then this degree equals the size of M(G_K). We give a partial answer to a question of Angel, Kechris and Lyons showing that if K is a relational Ramsey class and G_K is amenable, then M(G_K) admits a unique invariant Borel probability measure that is concentrated on a unique generic orbit.

math.LO↗

arXiv2013

The Fine Classification of Conjunctive Queries and Parameterized Logarithmic Space Complexity

We perform a fundamental investigation of the complexity of conjunctive query evaluation from the perspective of parameterized complexity. We classify sets of boolean conjunctive queries according to the complexity of this problem. Previous work showed that a set of conjunctive queries is fixed-parameter tractable precisely when the set is equivalent to a set of queries having bounded treewidth. We present a fine classification of query sets up to parameterized logarithmic space reduction. We show that, in the bounded treewidth regime, there are three complexity degrees and that the properties that determine the degree of a query set are bounded pathwidth and bounded tree depth. We also engage in a study of the two higher degrees via logarithmic space machine characterizations and complete problems. Our work yields a significantly richer perspective on the complexity of conjunctive queries and, at the same time, suggests new avenues of research in parameterized complexity.

cs.CC↗

arXiv2013

An Algebraic Preservation Theorem for Aleph-Zero Categorical Quantified Constraint Satisfaction

We prove an algebraic preservation theorem for positive Horn definability in aleph-zero categorical structures. In particular, we define and study a construction which we call the periodic power of a structure, and define a periomorphism of a structure to be a homomorphism from the periodic power of the structure to the structure itself. Our preservation theorem states that, over an aleph-zero categorical structure, a relation is positive Horn definable if and only if it is preserved by all periomorphisms of the structure. We give applications of this theorem, including a new proof of the known complexity classification of quantified constraint satisfaction on equality templates.

cs.LO↗