Algorithms, Theory, Logic

This field investigates a range of theoretical and practical aspects of algorithmics. Considering all aspects of the process holistically—from analyzing the efficiency and the quality of the solutions, to developing provably efficient and correct software, to packaging and releasing this software—helps to inform the research as well as benefit the community.

Groups and Researchers in this Field


Principles of Security and Privacy

Gilles Barthe's research interests lie in the areas of programming languages and program verification, software and system security, cryptography, formal methods and logic. His goal is to develop foundations and tools for reasoning about security and privacy properties of algorithms and implementations. His recent work focuses on building relational verification methods for probabilistic programs and on their applications in cryptography and privacy. He is also interested in provably secure countermeasures against side-channel attacks. Read more

Gilles Barthe

Gilles Barthe

MPI-SP, Scientific Director

Fine-Grained Complexity and Algorithms

Karl Bringmann leads the group Fine-Grained Complexity and Algorithms in the Algorithms and Complexity department at the Max Planck Institute for Informatics. He is interested in the inherent time complexity of combinatorial problems. Specifically, which problems can be solved in near-linear time, which require quadratic time, etc.? Since NP-hardness is too coarse to answer such questions, the modern approach is to prove conditional lower bounds via fine-grained reductions from certain hardness assumptions; this approach is called fine-grained complexity theory. Karl’s group develops this theory and uses a combination of fine-grained lower bounds and algorithm design to determine the optimal time complexity of various problems from computational geometry, stringology, graph theory, and optimization. Read more

Karl Bringmann

Karl Bringmann

MPI-INF, Senior Researcher

Foundations of Programming

Derek Dreyer leads the Foundations of Programming group at the Max Planck Institute for Software Systems. The group focuses on the design, semantics, verification, and implementation of modern programming languages and systems. Topics of study have included advanced type systems for modular programming and verification; Kripke models and separation logics for reasoning about higher-order, imperative, and concurrent programs; and compositional compiler certification. Derek is interested in developing a “realistic” theory of modularity—figuring out how we can build and reason modularly about programs that use features like fine-grained concurrency, higher-order state, recursive linking, dependent types, or self-modifying assembly code, meaning traditional semantic and verification techniques cannot account for them. Read more

Derek Dreyer

Derek Dreyer

MPI-SWS, Faculty

Foundations of Computer Security

Deepak Garg’s interests include computer security and privacy, formal logic, and programming languages. He is head of the Foundations of Computer Security group, associated with both the Security & Privacy and the Programming Languages & Verification research areas at the Max Planck Institute for Software Systems. The group’s current projects investigate tracking and controlling flows of sensitive information through Web browsers, using type systems to statically estimate the asymptotic complexity of incremental runs of programs, creating mechanisms to enforce data protection policies across multiple system infrastructure layers, extending separation logics to reason about security protocols, and developing foundations and algorithms for temporal logic-based privacy audits of legal compliance, among others. Read more

Deepak Garg

Deepak Garg

MPI-SWS, Faculty

Geometric Complexity Theory

Computational complexity theory is concerned with the study of the inherent complexity of computational problems. Its flagship conjecture is the famous “P not equal NP” conjecture. Classical algebraic complexity theory relates this conjecture to deep questions in algebra. A recent new approach is to incorporate methods from algebraic geometry and representation theory to make progress on this and many related conjectures. This area is called Geometric Complexity Theory and it involves for example the construction of normal forms for algebraic computation, the analysis of symmetries of complete polynomial families, and the study of the representation theory of the coordinate rings of specific group varieties. Christian Ikenmeyer leads the research group that is working on these topics. Read more

Christian Ikenmeyer

Christian Ikenmeyer

MPI-SWS, Research Group Leader

Discrete Optimization

Discrete optimization problems are ubiquitous. Whenever there is a choice between several possibilities, there is an inherent optimization problem. Our core competence in this area is to recognize such optimization problems, to establish mathematical models, to tackle them by state-of-the-art methods, and to invent new techniques to obtain satisfactory results.  Our research is application-driven. This also includes inter-disciplinary research with collaborators from engineering, physics, chemistry, biology, economics, etc. Read more

Andreas Karrenbauer

Andreas Karrenbauer

MPI-INF, Senior Researcher

Theory of Distributed Systems

Christoph Lenzen coordinates the Theory of Distributed Systems research area in the Algorithms and Complexity Department at the Max Planck Institute for Informatics. Broadly, distributed computing concerns systems of multiple agents that act based on local information. Typical problems require agents to collaboratively solve a task quickly, despite limits on communication, faults, or inaccurate data. The group’s approach is largely based on tools of theoretical computer science. They devise abstract models to capture problems’ central challenges, and prove upper and lower bounds on the complexity of solutions in terms of the amount of communication, number of faults that can be tolerated, etc. They also seek to provide prototype implementations of their algorithms, which may then form a basis for applications. Read more

Christoph Lenzen

Christoph Lenzen

MPI-INF, Senior Researcher

Rigorous Software Engineering

Rupak Majumdar is a Scientific Director at the Max Planck Institute for Software Systems, where he leads the Rigorous Software Engineering group. His main research interests include verification and control of reactive, real-time, hybrid, and probabilistic systems, software verification and programming languages, logic, and automata theory. His group investigates both foundational principles and practical tools for the design and analysis of computer systems. Some recent research directions have included methodologies and tools for the automated co-design of embedded controllers and their implementations, foundations of robustness for hybrid systems, scalable tools for coverability analysis of Petri nets, algorithms for the analysis of infinite-state systems, and verification of asynchronous programs. Read more

Rupak Majumdar

Rupak Majumdar

MPI-SWS, Faculty

Algorithms and Complexity

Kurt Mehlhorn is known for many research contributions in a wide variety of areas, among them algorithms, complexity, and optimization, as well as for his work on software including LEDA. In addition to being a director of the Max Planck Institute for Computer Science, he heads its Algorithms & Complexity Department, which takes a holistic approach to studying theoretical and practical aspects of modern algorithmics: from designing new algorithms and algorithmic techniques, analyzing their efficiency and the quality of their solutions, and developing provably efficient and correct software, to packaging the programs in software libraries. He is also a Principal Investigator at the Cluster of Excellence on Multimodal Computing and Interaction, and a director of the Indo-German Max Planck Center for Computer Science. Read more

Kurt Mehlhorn

Kurt Mehlhorn

MPI-INF, Scientific Director

Foundations of Algorithmic Verification

Joel Ouaknine is a Scientific Director at the Max Planck Institute for Software Systems, where he leads the Foundations of Algorithmic Verification group. He also holds secondary appointments at Saarland University and Oxford University. His research interests span a range of topics broadly connected to algorithmic verification and theoretical computer science. His group's recent focus has been on decision and synthesis problems for linear dynamical systems (both continuous and discrete), making use among others of tools from number theory, Diophantine geometry, and real algebraic geometry. Other interests include the algorithmic analysis of real-time, probabilistic, and infinite-state systems (e.g. model-checking algorithms, synthesis problems, complexity), logic and applications to verification, automated software analysis, and concurrency.  Read more

Joel Ouaknine

Joel Ouaknine

MPI-SWS, Faculty

Software Analysis and Verification

Viktor Vafeiadis leads the Software Analysis and Verification research group at the Max Planck Institute for Software Systems. The group’s research concerns the development of mathematical theories and tools for formally reasoning about software. It aims to improve software quality by making it possible to build provably correct software components. This involves coming up with rigorous mathematical specifications of software components, developing custom proof techniques for proving adherence to those specifications, and improving the underlying general-purpose verification infrastructure. Much of their work focuses on reasoning about concurrent programs; another important aspect of their work concerns the Coq interactive theorem prover and improving its applicability for reasoning about software. Read more

Viktor Vafeiadis

Viktor Vafeiadis

MPI-SWS, Faculty

Automation of Logic

Christoph Weidenbach leads the Automation of Logic research group at the Max Planck Institute for Informatics. The group’s work ranges from basic research on (new) logics and their automation up to applications in research and industry. Topics of interest include propositional and first-order logics and their combination with theories, arithmetic, decidable fragments for knowledge representation and reasoning, and fragments of higher-order logics. Results are reflected in system development including prototypical reasoning support for higher-order systems, as well as reasoning engines that are deployed in industrial practice. Example applications are verification of hardware and software, distributed systems analysis, query answering with respect to knowledge bases, product modeling and optimization, and biochemical process analysis. Read more

Christoph Weidenbach

Christoph Weidenbach

MPI-INF, Senior Researcher

Models of Computation

Georg Zetzsche leads the Models of Computation research group at the Max Planck Institute for Software Systems.  The group studies abstract models of computations, how to analyze them algorithmically, and how to use them to represent program behavior.  Topics of interest are therefore decidability, complexity, and expressiveness of infinite-state systems. The studied models of computation include concurrent systems such as Petri nets and other counter machines, but also models of recursion such as (higher-order) pushdown automata. The group applies methods from automata theory, formal languages, and logic, but also semigroup and group theory.  Currently in focus are the synthesis of finite-state abstractions of infinite-state systems, such as closure computation and separability problems, and also algorithmic problems for infinite groups. Read more

Georg Zetzsche

Georg Zetzsche

MPI-SWS, Faculty

Research at Partner Universities