Research

My research interests are at the intersection of mathematics and computer science. At the center of my research is the application of logical and complexity theoretic methods to computer science scenarios, in particular to database theory and verification.

Querying Dynamic Databases

Extracting information from enormous amounts of data that is updated frequently is a considerable challenge in many disciplines. Dynamic complexity theory studies the theoretical foundations of logical query languages for databases that are subjected to frequent changes. In this area, one of the main goals is to develop a theory for classifying queries with respect to the amount of resources necessary for their dynamic evaluation.

In my research, I study (a) methods for determining the amount of resources necessary for maintaining queries in this dynamic context, and (b) explore the structure of small dynamic complexity classes as well as their relation to traditional static complexity classes.

A good start to the area:

 

Logics for Specification and Verification

Automated verification of software and hardware is an important task. Often intended properties of a system are specified by logical formalisms that navigate along traces of the system. Similar formalisms are the basis for query languages for extracting information from XML documents and graph databases.

In my research, I explore logical systems with respect to their applicability for such tasks. I contributed to the design of a navigational logic, DataLTL, that allows for specifying complex properties of systems with many processes, and whose basic reasoning tasks remain decidable. For another basic specification language, the two-variable fragment of predicate logic, we study the complexity of reasoning tasks for many variants and were able to give a classification of their computational complexity

Selected papers

 

A Web-based System for Learning Logic

A typical application of logics in computer science is to model a real world scenario, formulate formulas expressing knowledge about the scenario, and to infer new knowledge by logical reasoning. While there is no shortage on software for logics, a closer look reveals that there is almost no up-to-date, intuitive software system for assisting the learning process of students for such basic teaching goals.

We aim at building such an interactive web-based system with support for those tasks for traditional logics (propositional logic, modal logics and predicate logic) but also more domain specific logics used for verification and database query tasks.

Try it: Logic Web Tutorial

Introduction to the System: 

 

Publications

An up-to-date list of my publications can be found here: DBLP