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Faculty of Mathematics, Physics & Computer Science

Theoretical Computer Science (AI VII) – Prof. Dr. Wim Martens

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Research

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Principles of Data Management

Data is around us in all shapes and sizes. We do fundamental research about how to store data and how to query it. This research leads us to questions about efficient evaluation algorithms, query optimization, expressive power, and the fundamental complexity of computational problems. 

Selected topics:

  • Graph Query Languages
  • Pattern Languages for Querying Graphs and Trees
  • Enumeration Problems
  • Query Analysis​
  • Information Extraction​

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Formal Languages and Automata Theory

At the core of our research questions (e.g., on data management or internet standarization) we often find fundamental questions about formal language theory. We encounter questions about regular languages, finite automata, or tree automata. 

Selected topics:

  • Tree Languages and Tree Automata
  • Regular Expressions
  • Determinism versus Nondeterminism
  • Separability and Language Decomposition Problems
  • Enumeration Problems

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Data Standards and Query Languages

We always need to keep an eye on the current developments concerning standards in data management. The development of a standard is a non-trivial and sometimes long process. From time to time, it needs input from academia to ensure that design decisions are well motivated. The interaction between theory and practice can be very fruitful in this area.

Selected topics:

  • Foundations of Internet Technology (W3C standards)
  • Graph-structured Data (SPARQL, Cypher)
  • Tree-structured Data (XML, JSON, XPath)​

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Schema Languages

Throughout the years, we have gathered a particular expertise in schema languages for tree structured, graph structured, or grid structured data. Our emphasis is on understanding the "bare bones" principles of the languages in question.

Selected topics:

  • XML Schema, Relax NG (and BonXai)
  • Tabular Data (Sculpt)


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Software Tools and Prototypes

Theoretical ideas sometimes need to be confronted with reality. Such confrontation is useful for testing if an idea works in practical settings, explaining why typical practical cases behave more nicely than what "worst-case analysis" shows, or for generating new and practically relevant research questions.

Selected topics:

  • DARQL - Deep Analysis of SPARQL Queries
  • Chisel - A Tool for Validation and Tranformation of CSV-like Data
  • BonXai - A Pattern based XML Schema Language

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