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The research focus of the ``Formal Methods and Theoretical Computer Science'' group is the development of provably correct procedures for the verification and analysis of complex systems.
The goal of our research is to identify frameworks under which efficient automatic verification procedures for complex systems exist. In doing so, we investigate possibilities to exploit modularity in verification on different levels, e.g.: Possibilities for efficient modular reasoning in complex logical theories, and modeling and modular verification of complex systems in general.
Our theoretical contributions form the basis for the development of practically applicable tools for the verification of safety-critical systems, in particular in the context of the SFB Transregio project AVACS (Automatic Verification and Analysis of Complex Systems). We use our methods both in program verification and to verify various control systems (e.g., radio controllers for train systems, or hybrid control systems for chemical plants). We also apply our approaches in cryptography, databases, or mathematics.
Research
Our research focuses on the modular verification of complex systems; of particular interest is modular reasoning in complex theories. We analyze various application areas.
Reasoning in complex theories
The problems which arise in deductive verification, but also in other fields (such as mathematics, databases and cryptography) often involve reasoning in combinations of theories. A large part of our research is therefore devoted to finding methods for efficient reasoning in complex theories.
Modeling and verification of complex systems
For verifying complex systems, we modularly reduce the verification tasks for the full complex systems to simpler verification tasks for their component parts, taking interaction into account. For the verification of the individual systems we use e.g. deductive verification techniques or techniques based on abstraction/refinement.
Applications
In our research we aim at developing general methods, which can be used in a wide variety of application domains:
Verification: We analyzed the applicability of the methods we developed on various examples from the verification of reactive, real-time and hybrid systems (which we analyze in the AVACS project), in particular for increasingly more complex controllers of systems of trains, cars, and for chemical plants.