Annual Report 2010 - Fachgruppe Informatik an der RWTH Aachen ...

Overview
The research group on Mathematical Foundations of Computer Science is part of the
Department of Mathematics, but there is a very intensive collaboration, both in research and
teaching, with the Department of Computer Science, most notably with the research group
Computer Science 7 (Prof. Wolfgang Thomas).
The main research areas of the group are mathematical logic and the theory of infinite games,
with particular emphasis on algorithmic issues in logical systems, computational model
theory, fixed point logics, and strategy construction and definability in infinite games.
Research Projects
Games for Design and Verification (GAMES)
E. Grädel, D. Fischer, T. Ganzow, Ł. Kaiser, M. Ummels
GAMES is a Research Networking Programme funded by the European Science Foundation
(ESF). It was launched in March 2008 for a duration of five years and is directed by Erich
Grädel.
The GAMES network proposes a research and training programme for the design and
verification of computing systems, using a methodological framework that is based on the
interplay of finite and infinite games, mathematical logic and automata theory. This ESF
networking programme is the continuation of the European Research Training Network
Games and Automata for Synthesis and Validation (GAMES) that had been funded under the
Fifth Framework Programme of the European Community from 2002 to 2006, but it is
scientifically broader and more ambitious.
It includes about 150 researchers throughout Europe.
Computational Model Theory and Descriptive Complexity
E. Grädel, T. Ganzow
Finite model theory studies the relationship between logical definability and computational
complexity on finite structures. A particularly important aspect concerns logical descriptions
of complexity classes. Our research group has made significant contributions to this area.
A newer development in this field is the extension of the approach and methodology of finite
model theory to (particular classes of) infinite structures. Algorithmic issues on infinite
structures are of increasing importance in several areas of computer science. In databases, the
traditional model based on finite relational structures has turned out to be inadequate for
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