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Bachelor (contact: Ulrich Loup)

Given a set of polynomials of arbitrary degree and in several variables, we are interested in its set of common zeros, i.e. the solutions to the corresponding system of polynomial equations, called variety. A Gröbner basis of a set of polynomials is another set of polynomials which have the same common zeros, but reduced with respect to division by each other. Well-established algorithms can compute a Gröbner basis which is also minimal in the sense that none of its elements is redundant, i.e., it can not be reduced to zero by means of the other basis elements.

Gröbner bases have many important applications, e.g., the ideal membership, equality or emptiness problems. Most importantly in our context is Hilbert's Nullstellensatz. This famous result from algebraic geometry entails that if a set of polynomials has an empty variety, its Gröbner basis contains exclusively a constant. Moreover, the converse is also true: If the respective Gröbner basis is nonempty, the corresponding variety is likewise. However, this result considers all possible zeros of polynomials, in particular, the complex ones.

Hilbert's Nullstellensatz, a famous result from algebraic geometry, entails that if a set of polynomials has an empty variety, its Gröbner basis contains exclusively a constant. Moreover, the converse is also true: If the respective Gröbner basis is nonempty, the corresponding variety is likewise. However, this result considers all possible zeros of polynomials, in particular, the complex ones.

Our special interest lies in real varieties. Hence, we need to make use of the Real Nullstellensatz, a variant of Hilbert's Nullstellensatz specialized to real solutions, in order to use the Gröbner-basis approach for solving a polynomial equation system.

This thesis topic comprises two major aspects: First, an application of the Real Nullstellensatz shall be implemented on the basis of existing methods for Gröbner basis computations. Second, our implementation of algorithms to compute Gröbner bases shall be enhanced to speed up the whole computation.

BSc/MSc/Diploma Topics
Teaching WS 2012/13
Hybrid Systems Group

We are looking for a HiWi for the Compiler Construction course. If you are interested, please contact Thomas Noll.

Joost-Pieter Katoen has been appointed as a member of the renowned Academia Europaea (Academy of Europe), a European, non-governmental association acting as an Academy whose members are scientists and scholars who collectively aim to promote learning, education and research.

Vacancies for postdoctoral researchers in "Automated Analysis of Probabilistic Programs". Application deadline: August 15, 2013.

Joost-Pieter Katoen has been awarded a Distinguished Professorship from the RWTH Aachen University.

The Hybrid Systems: Computation and Control (HSCC'13) conference in Philadelphia has been very successful: Hongfei Fu received the best student paper award for his paper "Approximating acceptance probabilities of CTMC-paths on multi-clock deterministic timed automata". Besides, the paper by Ilya Tkachev, Alexandru Mereacre, Alessandro Abate and Joost-Pieter Katoen was ranked second in the overall best paper award selection.

Joost-Pieter Katoen has been elected as Steering Committee Chair of ETAPS (www.etaps.org), the largest conference on theory and practice of software in Europe. He is the first non-UK ETAPS SC chair since the conference was initiated in 1998. More information here.

The Alumni-Magazine of RWTH Aachen University contains an interview with our former PhD student and postdoctoral researcher, Dr. Tingting Han.

HiWi's wanted to work in a new European Space Agency project for enhancing state-of-the-art design and analysis tools (COMPASS) for the next generation European rockets. Need programming and model checking affinity. See here for details and contact.

We offer openings for several PhD candidates in the area of
"Model-Based Design and Analysis for Dependable Software Systems". Deadline for application: September 14, 2012. For further information click here.

The Theory of Hybrid Systems Group offers two jobs as student assistants within the CEBug project. For more information, look here.

Dino Distefano received the prestigious Roger Needham Award for his work on software verification. This award is for a distinguished research contribution in computer science by a UK based researcher who has completed up to 10 years of post-doctoral research. Dr. Distefano was the first PhD student supervised by Joost-Pieter Katoen.

Marijn Jongerden received the German MMB (Messung, Modellierung und Bewertung von Rechensystemen) Award 2012 of the GI/ITG-Committee for Measurement, Modelling and Evaluation of Computing Systems for his PhD-thesis on "Model-based energy analysis of battery powered systems". His work was supervised by Boudewijn Haverkort (Twente) and Joost-Pieter Katoen.

Our paper "Formal Correctness, Safety, Dependability and Performance Analysis of a Satellite" has been accepted to ICSE 2012 in the track SE in Practice (18% acceptance rate). The paper treats a new satellite from the European Space Agency that was modeled and analyzed with modern tools during the actual satellite design.

Joost-Pieter Katoen will act as DJ in the "Nacht der Professoren" in the Apollo bar and cinema.