Nicole Schweikardt

Luisa Gerlach, Tobias Köppl, René Zander et al.

We address the problem of checking query containment, a foundational problem in database research. Although extensively studied in theory research, optimization opportunities arising from query containment are not fully leveraged in commercial database systems, due to the high computational complexity and sometimes even undecidability of the underlying decision problem. In this article, we present the first approach to applying quantum computing to the query containment problem for conjunctive queries under set semantics. We propose a novel formulation as an optimization problem that can be solved on gate-based quantum hardware, and in some cases directly maps to quantum annealers. We formally prove this formulation to be correct and present a prototype implementation which we evaluate using simulator software as well as quantum devices. Our experiments successfully demonstrate that our approach is sound and scales within the current limitations of quantum hardware. In doing so, we show that quantum optimization can effectively address this problem. Thereby, we contribute a new computational perspective on the query containment problem.

Markus L. Schmid, Nicole Schweikardt

The regular spanners (characterised by vset-automata) are closed under the algebraic operations of union, join and projection, and have desirable algorithmic properties. The core spanners (introduced by Fagin, Kimelfeld, Reiss, and Vansummeren (PODS 2013, JACM 2015) as a formalisation of the core functionality of the query language AQL used in IBM's SystemT) additionally need string-equality selections and it has been shown by Freydenberger and Holldack (ICDT 2016, Theory of Computing Systems 2018) that this leads to high complexity and even undecidability of the typical problems in static analysis and query evaluation. We propose an alternative approach to core spanners: by incorporating the string-equality selections directly into the regular language that represents the underlying regular spanner (instead of treating it as an algebraic operation on the table extracted by the regular spanner), we obtain a fragment of core spanners that, while having slightly weaker expressive power than the full class of core spanners, arguably still covers the intuitive applications of string-equality selections for information extraction and has much better upper complexity bounds of the typical problems in static analysis and query evaluation.

Steffen van Bergerem, Nicole Schweikardt

We consider weighted structures, which extend ordinary relational structures by assigning weights, i.e. elements from a particular group or ring, to tuples present in the structure. We introduce an extension of first-order logic that allows to aggregate weights of tuples, compare such aggregates, and use them to build more complex formulas. We provide locality properties of fragments of this logic including Feferman-Vaught decompositions and a Gaifman normal form for a fragment called FOW1, as well as a localisation theorem for a larger fragment called FOWA1. This fragment can express concepts from various machine learning scenarios. Using the locality properties, we show that concepts definable in FOWA1 over a weighted background structure of at most polylogarithmic degree are agnostically PAC-learnable in polylogarithmic time after pseudo-linear time preprocessing.