Thomas Zeume's research while affiliated with Ruhr-Universität Bochum and other places
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Publications (45)
We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We show that the emptiness problem for these automata is decidable. As an application, we p...
The regular languages with a neutral letter expressible in first-order logic with one alternation are characterized. Specifically, it is shown that if an arbitrary $\Sigma_2$ formula defines a regular language with a neutral letter, then there is an equivalent $\Sigma_2$ formula that only uses the order predicate. This shows that the so-called Cent...
Given a graph whose nodes may be coloured red, the parity of the number of
red nodes can easily be maintained with first-order update rules in the dynamic
complexity framework DynFO of Patnaik and Immerman. Can this be generalised to
other or even all queries that are definable in first-order logic extended by
parity quantifiers? We consider the qu...
The Iltis project provides an interactive, web-based system for teaching the foundations of formal methods. It is designed to allow modular addition of educational tasks as well as to provide immediate and comprehensive feedback. Currently, exercises for various aspects of typical automated reasoning workflows for propositional logic, modal logic,...
Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic,...
Which amount of parallel resources is needed for updating a query result after changing an input? In this work we study the amount of work required for dynamically answering membership and range queries for formal languages in parallel constant time with polynomially many processors. As a prerequisite, we propose a framework for specifying dynamic,...
We introduce a model of register automata over infinite trees with extrema constraints. Such an automaton can store elements of a linearly ordered domain in its registers, and can compare those values to the suprema and infima of register values in subtrees. We show that the emptiness problem for these automata is decidable. As an application, we p...
How can the result of a query be updated after changing a database? This is a fundamental task for database management systems which ideally takes previously computed information into account. In dynamic complexity theory, it is studied from a theoretical perspective where updates are specified by rules written in first-order logic.
In this article...
![Illustration of the CQs q3 and q3′\documentclass[12pt]{minimal}...](publication/333010284/figure/fig4/AS:960039598686218@1605902685162/Illustration-of-the-CQs-q3-and-q3documentclass12ptminimal-usepackageamsmath_Q320.jpg)
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. Approximating a hard CQ by a query from such a fragment can thus allow for an efficient approximate evaluation. While underapproximations (i.e., approximations that return correct answers only) are well-understood, the dual notion of ove...
We consider fragments of the description logic SHOIF extended with regular expressions on roles. Our main result is that satisfiability and finite satisfiability are decidable in two fragments SHOIF^1 and SHOIF^2, NExpTime-complete for the former and in 2NExpTime for the more expressive latter fragment. Both fragments impose restrictions on regular...
In 2015, it was shown that reachability for arbitrary directed graphs can be updated by first-order formulas after inserting or deleting single edges. Later, in 2018, this was extended for changes of size $\frac{\log n}{\log \log n}$, where $n$ is the size of the graph. Changes of polylogarithmic size can be handled when also majority quantifiers m...
Dynamic Complexity studies the maintainability of queries with logical formulas in a setting where the underlying structure or database changes over time. Most often, these formulas are from first-order logic, giving rise to the dynamic complexity class DynFO. This paper investigates extensions of DynFO in the spirit of parameterised algorithms. In...
Given a graph whose nodes may be coloured red, the parity of the number of red nodes can easily be maintained with first-order update rules in the dynamic complexity framework DynFO of Patnaik and Immerman. Can this be generalised to other or even all queries that are definable in first-order logic extended by parity quantifiers? We consider the qu...
Iltis is an interactive, web-based system for teaching logic. It is designed to provide immediate and comprehensive feedback for exercises covering various aspects of the reasoning workflow. This poster presentation reports on new exercises and feedback mechanisms for modal and first-order logic.
Conjunctive query (CQ) evaluation is NP-complete, but becomes tractable for fragments of bounded hypertreewidth. Approximating a hard CQ by a query from such a fragment can thus allow for an efficient approximate evaluation. While underapproximations (i.e., approximations that return correct answers only) are well-understood, the dual notion of ove...
Patnaik and Immerman introduced the dynamic complexity class DynFO of database queries that can be maintained by first-order dynamic programs with the help of auxiliary relations under insertions and deletions of edges. This article confirms their conjecture that the reachability query is in DynFO.
As a byproduct, it is shown that the rank of a mat...
Most projects that create innovations in Computer Science education, whether they be changes to content or pedagogy, focus on first developing materials and then proving effectiveness. For educational innovations to have impact, however, they must be adopted by other instructors. Getting instructors to use new educational strategies is a significan...
In this report, we survey the existing scholarship in STEM higher education regarding what motivates, encourages, and inhibits educators' decisions to adopt teaching innovations. After reviewing common theoretical foundations and considerations for adoption and dissemination studies, we identify challenges for encouraging adoption among educators i...
Recently it was shown that the transitive closure of a directed graph can be updated using first-order formulas after insertions and deletions of single edges in the dynamic descriptive complexity framework by Dong, Su, and Topor, and Patnaik and Immerman. In other words, Reachability is in DynFO. In this article we extend the framework to changes...
Logic is a foundation for many modern areas of computer science. In artificial intelligence, as a basis of database query languages, as well as in formal software and hardware verification — modelling scenarios using logical formalisms and inferring new knowledge are important skills for going-to-be computer scientists.
The Iltis project aims at pr...
In the setting of DynFO, dynamic programs update the stored result of a query
whenever the underlying data changes. This update is expressed in terms of
first-order logic. We introduce a strategy for constructing dynamic programs
that utilises periodic computation of auxiliary data from scratch and the
ability to maintain a query for a limited numb...
The article investigates classes of queries maintainable by conjunctive queries (CQs) and their extensions and restrictions in the dynamic complexity framework of Patnaik and Immerman. Starting from the basic language of quantifier-free conjunctions of positive atoms, it studies the impact of additional operators and features - such as union, atomi...
In this work the dynamic descriptive complexity of the k-clique query is studied. It is shown that when edges may only be inserted then k-clique can be maintained by a quantifier-free update program of arity , but it cannot be maintained by a quantifier-free update program of arity (even in the presence of unary auxiliary functions). This establish...
In the traditional static setting, several methods for proving inexpressibility results have been developed.
One of the major goals of descriptive complexity theory is to study the relationship of the expressive power of various logics. The motivation is that results relating the expressive power of logics may help to answer questions like “Is a given query expressible in some logic?” more easily. It may also help to explain why it is hard to express a gi...
In this chapter the dynamic complexity framework is defined formally; and many examples for its expressive power are presented. As the dynamic complexity framework is based on notions from database theory and finite model theory, we will shortly review necessary foundations from those two areas first. Afterwards we will introduce the formal dynamic...
In the decade after its introduction in the early 1990s, dynamic descriptive complexity has seen many results; including results for the maintainability of specific queries as well as lower bounds for restricted dynamic programs. Yet, after Hesse’s proof that reachability can be maintained in \(\textsc {DynTC} ^0\) [Hes03b], work in the area stoppe...
In the setting of dynamic complexity, the goal of a dynamic program is to maintain the result of a fixed query for an input database that is subject to changes, possibly using additional auxiliary relations. In other words, a dynamic program updates a materialized view whenever a base relation is changed. The update of query result and auxiliary re...
In many of today’s data management scenarios the data is subject to frequent modifications, and it is often essential to react to those changes quickly. When a train is canceled on short notice, travelers need to find alternative connections as fast as possible. When a web server is temporarily not available, data packages have to be rerouted immed...
In many data management scenarios the data is subject to frequent modifications, and it is often essential to react to those changes quickly. When a train is canceled on short notice, travelers need to find alternative connections as fast as possible. When a web server is temporarily not available, data packages have to be rerouted immediately.
It is shown that order-invariance of two-variable first-logic is decidable in the finite. This is an immediate consequence of a decision procedure obtained for the finite satisfiability problem for existential second-order logic with two first-order variables ($\mathrm{ESO}^2$) on structures with two linear orders and one induced successor. We also...
Graph databases in many applications---semantic web, transport or biological
networks among others---are not only large, but also frequently modified.
Evaluating graph queries in this dynamic context is a challenging task, as
those queries often combine first-order and navigational features.
Motivated by recent results on maintaining dynamic reacha...
A dynamic program, as introduced by Patnaik and Immerman (1994), maintains
the result of a fixed query for an input database which is subject to tuple
insertions and deletions. It can use an auxiliary database whose relations are
updated via first-order formulas upon modifications of the input database. This
paper studies static analysis problems f...
We consider the dynamic complexity of some central graph problems such as
Reachability and Matching and linear algebraic problems such as Rank and
Inverse. As elementary change operations we allow insertion and deletion of
edges of a graph and the modification of a single entry in a matrix, and we are
interested in the complexity of maintaining a p...
The re-evaluation of a query result after modifying a large database can be a time-consuming process; in particular when it is performed from scratch. For this reason previously computed information such as the old query result and (possibly) other auxiliary information is often reused in order to speed up the process. In this thesis, dynamic query...
In this work the dynamic descriptive complexity of the k-clique query is studied in a framework introduced by Patnaik and Immerman. It is shown that when edges may only be inserted then k-clique can be maintained by a quantifier-free update program of arity k − 1, but it cannot be maintained by a quantifier-free update program of arity k − 2 (even...
This paper continues the study of the two-variable fragment of first-order logic (FO2) over two-dimensional structures, more precisely structures with two orders, their induced successor relations and arbitrarily many unary relations. Our main focus is on ordered data words which are finite sequences from the set ×D where is a finite alphabet and D...
The finite satisfiability problem of two-variable logic extended by a linear
order successor and a preorder successor is shown to be undecidable.
The dynamic complexity of the reachability query is studied in the dynamic
complexity framework of Patnaik and Immerman, restricted to quantifier-free
update formulas.
It is shown that, with this restriction, the reachability query cannot be
dynamically maintained, neither with binary auxiliary relations nor with unary
auxiliary functions, and that...
It is shown that the finite satisfiability problem for two-variable logic
over structures with one total preorder relation, its induced successor
relation, one linear order relation and some further unary relations is
EXPSPACE-complete. Actually, EXPSPACE-completeness already holds for structures
that do not include the induced successor relation....
The paper proposes and studies temporal logics for attributed words, that is,
data words with a (finite) set of (attribute,value)-pairs at each position. It
considers a basic logic which is a semantical fragment of the logic
$LTL^\downarrow_1$ of Demri and Lazic with operators for navigation into the
future and the past. By reduction to the emptine...
The finite satisfiability problem for two-variable logic over structures with unary relations and two order relations is investigated.
Firstly, decidability is shown for structures with one total preorder relation and one linear order relation. More specifically,
we show that this problem is complete for EXPSPACE. As a consequence, the same upper b...
Citations
... Our proof is much more elementary, and uses only the most basic facts about finite automata. 1 We use 'string' and 'word' interchangeably. ...
... It is yet to be seen whether this could be useful for real-world systems, however, some recent work has looked at applying dynamic complexity. Schmidt, Schwentick, Tantau, Vortmeier and Zeume [103] studied the amount of parallel work needed to maintain an answer to certain questions (such as range queries) over words that are subject to updates. Chapter 6. ...
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... We introduce some concepts and notation that we need throughout the paper. See also [21] for an overview of Dynamic Complexity. We assume familiarity with first-order logic FO, and refer to [18] for basics of Finite Model Theory. ...
... We now shortly recapitulate the dynamic complexity framework as introduced by Patnaik and Immerman [PI97], and refer to Reference [SZ16] for details. ...
Reference: Dynamic Complexity of Parity Exists Queries
... However, we demonstrate that this problem can be effectively reduced to finite KBSat for ZIQ, making the finite KBSat the main problem to study. We apply our methods to derive new results for extensions of ALC with transitive closure of roles (Jung, Lutz, and Zeume 2020) and to lift some known results about finite CQ entailment for various DLs to the setting of local queries. ...
... This is described in Section 4. Decidability then follows from the fact that the emptiness problem for parity automata is decidable [Rab72]. This article is the long version of [TZ20]. It in particular provides full proofs for all results. ...
... Además, facilita la lectura, escritura y Prácticas docentes de aula en la enseñanza del pensamiento computacional en escuelas medias oficiales y particulares de la región metropolitana de la Ciudad de Panamá REVISTA ANUAL, ACCIÓN Y REFLEXIÓN EDUCATIVA, N° 46 Enero, 2021 ISSN L 2644-3775 212 comprensión de especificaciones formales y su análisis (Mossakowski, 2010). Por otro lado, modelar escenarios utilizando formalismos lógicos e inferir nuevos conocimientos son habilidades importantes en el campo de la enseñanza de la informática (Geck et al., 2018). Por lo tanto, el aprendizaje de formalismos lógicos y, en particular, el modelado lógico es de suma importancia para los estudiantes de informática. ...
... Approximations of ontologies in tractable languages with stronger guarantees were recently studied in (Bötcher, Lutz, and Wolter 2019;Haga et al. 2020), but querying and data were (mostly) not considered. In database theory, approximate querying (without ontologies) was studied in (Fink and Olteanu 2011;Barceló, Libkin, and Romero 2014;Barceló, Romero, and Zeume 2018). The approximation and rewriting of OMQs in(to) datalog is studied in (Bienvenu et al. 2014;Kaminski, Nenov, and Grau 2016;Feier, Kuusisto, and Lutz 2019). ...
Reference: How to Approximate Ontology-Mediated Queries
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... Research presented in this paper includes evaluation of AI-generated results against human generated ground truth and a small user experience study. In line with a growing body of evidenced-based practices, the methodology employed strives to minimize bias and broaden potential impact within higher education contexts (Henderson et al., 2015;Taylor et al., 2018;Hovey & Barker, 2020;Petousi and Sifaki, 2020). ...
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... While dissemination of best practices at conferences and through papers remains one of the leading approaches to fostering the adoption of innovative teaching practices, there is limited evidence that such practices do little more than raise awareness of said innovations [1]. This is true even when innovative teaching practices have been proven to be effective [2]. ...
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