So-called ‘discrete dynamical systems’ form the basis for key computational challenges in a variety of fields, from program analysis and computer-aided verification to artificial intelligence and theoretical biology. Creating algorithmic solutions to make these systems amenable to automated verification techniques remains a major challenge. Researchers at the Max Planck Institute for Software Systems in Saarbrücken and the French ‘Centre National de la Recherche Scientifique’ are now working on advancing this automated verification approach with substantial funding by the European Research Council.

The interdisciplinary project, titled ‘Dynamical and Arithmetical Model Checking (DynAMiCs)’, is led by the three principal investigators—Professor Joël Ouaknine, Scientific Director at the Max Planck Institute for Software Systems (MPI-SWS) in Saarbrücken; Professor Florian Luca, also MPI-SWS and Stellenbosch University in South Africa; and Professor Valérie Berthé from the French ‘Institut de recherche en informatique fondamentale’ at the ‘Centre National de la Recherche Scientifique (CNRS)’ at the University Paris Cité.

“The paradigm of ‘model checking’ is a powerful method that allows us to automatically verify, with mathematical certainty, whether a system behaves as intended” says Prof. Joël Ouaknine. However, many discrete dynamical systems—systems that change over time following specific rules—cannot currently be verified with the available model-checking approaches.

One of the leading objectives of this new research project is thus to substantially broaden the classes of dynamical systems and properties that can be algorithmically handled via model checking. Specifically, it aims to tackle longstanding mathematical challenges, such as the Skolem Problem, that could lead to breakthroughs in understanding and verifying the behavior of other complex systems.

The Skolem Problem asks if, within a system following specific mathematical rules, a certain state will eventually be reached. Translated to other instances, this question could ask if a computer program will terminate under specific conditions, when an electric vehicle’s battery will fully deplete following a specific driving pattern, or if a manufacturing robot will reach a precise target after following programmed movements. Although seemingly simple, this mathematical problem has remained unsolved and has puzzled mathematicians and computer scientists alike for nearly a century.

Besides the Skolem Problem, the project also addresses additional longstanding mathematical challenges such as the Pisot Conjecture, piecewise-affine map reachability, and the Periodicity Conjecture. Addressing these complex problems demands innovative approaches that integrate insights from multiple areas of mathematics and computer science. “This funding allows us to leverage the interdisciplinary synergies between different fields, bringing together expertise that might not otherwise have come together,” says Florian Luca. The DynAMiCs project unites expertise in algorithmic verification led by Prof. Joël Ouaknine, symbolic dynamics under Prof. Valérie Berthé, and analytic number theory led by Prof. Florian Luca.

The project is funded via a European Research Council (ERC) Synergy Grant totaling 7.5 million euros over six years, with 5 million euros allocated to MPI-SWS. ERC Grants are among the most prestigious research awards globally, with Synergy Grants being especially competitive and offering the highest funding levels. In the current funding round, 548 proposals were submitted, of which only 57 were approved (10.4%).

 

Further Information:

Press Release by the European Research Council: https://erc.europa.eu/news-events/news/erc-2024-synergy-grants-results

List of Selected Projects: https://erc.europa.eu/sites/default/files/2024-11/erc-2024-syg-results-all-domains.pdf

 

Scientific Contact:

Professor Joël Ouaknine, PhD
Scientific Director at MPI SWS and Coordinating Principal Investigator of DynAMiCs
Max Planck Institute for Software Systems, Saarbrücken
Tel: +49 (0)681 9303 9701
E-Mail: joel@mpi-sws.org

Editor:

Philipp Zapf-Schramm
Max Planck Institute for Informatics
Tel: +49 681 9325 5409
E-Mail: pzs@mpi-inf.mpg.de

 

The paper "On the Decidability of Monadic Second-Order Logic with Arithmetic Predicates", by Valérie Berthé, Toghrul Karimov, Joris Nieuwveld, Joël Ouaknine, Mihir Vahanwala and James Worrell, was selected as one of 7 "Distinguished Papers" at LICS 2024.

Distinguished Paper awards are given to about 10% of papers at LICS. These are papers that, in the view of the LICS program committee, make exceptionally strong contribution to the field and should be read by a broad audience due their relevance, originality, significance and clarity.

Researchers from the Max Planck Institute for Software Systems (MPI-SWS) and the Max Planck Institute for Security and Privacy (MPI-SP) have authored a total of 7 papers accepted to POPL 2024.  This is the seventh year in a row that MPI-SWS researchers have published 5+ papers in POPL.  Congratulations to all our POPL authors!

• Decision and Complexity of Dolev-Yao Hyperproperties by Itsaka Rakotonirina, Gilles Barthe, Clara Schneidewind


• Parikh's Theorem Made Symbolic by Matthew Hague, Artur Jez, Anthony Widjaja Lin


• Positive Almost-Sure Termination – Complexity and Proof Rules by Rupak Majumdar and V.R. Sathiyanarayana.


• Ramsey Quantifiers in Linear Arithmetics by Pascal Bergsträßer, Moses Ganardi, Anthony Widjaja Lin, Georg Zetzsche


• Reachability in Continuous Pushdown VASS by A. R. Balasubramanian, Rupak Majumdar, Ramanathan S. Thinniyam, Georg Zetzsche


• Regular Abstractions for Array Systems by Chih-Duo Hong and Anthony Widjaja Lin


• Securing Verified IO Programs Against Unverified Code in F* by Cezar-Constantin Andrici, Stefan Ciobaca, Cătălin Hriţcu, Guido Martínez, Exequiel Rivas, Éric Tanter, Théo Winterhalter

Anne-Kathrin Schmuck has been appointed as new tenure-track faculty as of July 1st, 2023, after leading a prestigious externally funded Emmy-Noether research group hosted at MPI-SWS since 2020. Her group conducts fundamental research at the intersection of control engineering, cybernetics, and computer science to develop reliable and performant control software for cyber-physical systems. In particular, her work addresses the challenge of orchestrating continuous physical components and discrete logical decision making units within these highly automated and safety-critical technological systems.

Anne has been part of the MPI-SWS faculty as an independent research group leader since 2020. She holds a Dipl.-Ing. (M.Sc.) degree in engineering cybernetics from OvGU Magdeburg, Germany and a Dr.-Ing. (Ph.D.) degree in electrical engineering from TU Berlin, Germany. She joined MPI-SWS as a postdoctoral researcher in the area of formal methods in 2015.

MPI-SWS faculty member Derek Dreyer and nine of his collaborators (including notably UdS/MPI alumnus Ralf Jung, as well as former MPI-SWS postdocs Jacques-Henri Jourdan and Aaron Turon and UdS/MPI student David Swasey) have received the 2023 Alonzo Church Award for Outstanding Contributions to Logic and Computation for their seminal work on the Iris framework for higher-order concurrent separation logic, specifically the following four papers:

• Ralf Jung, David Swasey, Filip Sieczkowski, Kasper Svendsen, Aaron Turon, Lars Birkedal, Derek Dreyer: “Iris: Monoids and Invariants as an Orthogonal Basis for Concurrent Reasoning”. POPL 2015.
• Ralf Jung, Robbert Krebbers, Lars Birkedal, Derek Dreyer: “Higher-order ghost state”. ICFP 2016.
• Robbert Krebbers, Ralf Jung, Aleš Bizjak, Jacques-Henri Jourdan, Derek Dreyer, Lars Birkedal: “The Essence of Higher-Order Concurrent Separation Logic”. ESOP 2017.
• Ralf Jung, Robbert Krebbers, Jacques-Henri Jourdan, Aleš Bizjak, Lars Birkedal, Derek Dreyer: “Iris from the ground up: A modular foundation for higher-order concurrent separation logic”. J. Funct. Program. 28 (2018).

The Church Award has been given out since 2016, and has typically been given to papers that were 20-25 years old (to allow time for foundational work on logic to have major impact).  In this case, however, the four awarded Iris papers were published only 5-8 years ago! In that relatively short period of time, Iris has served as a springboard for a huge amount of research in semantics and program verification, including over 70 papers in top venues (see the Iris project page), and it has been adopted as a core verification technology by a multitude of research groups around the world, as well as the systems verification company BedRock Systems.

More details about the Alonzo Church Award and about the 2023 Church Award.

At ICALP 2023 and LICS 2023, two of the top conferences in logic and automata, there will be 6 papers by SWS researchers.

LICS 2023 (accepted papers: https://lics.siglog.org/lics23/accepted.php )

• Pascal Bergsträßer and Moses Ganardi. Revisiting Membership Problems in Subclasses of Rational Relations


• Faraz Ghahremani, Edon Kelmendi and Joël Ouaknine. Reachability in Injective Piecewise Affine Maps


• Toghrul Karimov, Edon Kelmendi, Joris Nieuwveld, Joël Ouaknine and James Worrell. The Power of Positivity

ICALP 2023 (accepted papers: https://icalp2023.cs.upb.de/accepted-papers/ )

• Marvin Künnemann, Filip Mazowiecki, Lia Schütze, Henry Sinclair-Banks and Karol Węgrzycki. Coverability in VASS Revisited: Improving Rackoff’s Bound to Obtain Conditional Optimality


• Pascal Baumann, Moses Ganardi, Rupak Majumdar, Ramanathan Thinniyam Srinivasan and Georg Zetzsche. Checking Refinement of Asynchronous Programs against Context-Free Specifications


• George Kenison, Joris Nieuwveld, Joël Ouaknine and James Worrell. Positivity Problems for Reversible Linear Recurrence Sequences

 

Kaushik Mallik's thesis, entitled Pushing the Barriers in Controller Synthesis for Cyber-Physical Systems, has been recognized with the 2023 ETAPS Doctoral Dissertation Award. The award is given to the PhD student who has made the most original and influential contribution to the research areas in the scope of the ETAPS conferences, and has graduated at a European academic institution. Kaushik was advised by MPI-SWS faculty member Rupak Majumdar.

This is the second time that the ETAPS Doctoral Dissertation Award was given to an MPI-SWS student. In 2021 it was awarded to Ralf Jung for his thesis on Understanding and Evolving the Rust Programming Language, supervised by Derek Dreyer.

Georg Zetzsche, head of the MPI-SWS Models of Computation group, has been awarded a 2022 ERC Starting Grant. Over the next five years, his project FINABIS will receive funding of 1.48 million euros for research on "Finite-state abstractions of infinite-state systems." Read more about the FINABIS project below.

In addition, MPI-SWS and University of Saarland alumnus Pramod Bhatotia, who is currently a professor at TU Munich, has also received a 2022 ERC Starting Grant for his project "DOS: A Decentralized Operating System".

ERC grants are the most prestigious and the most competitive European-level awards for ground-breaking scientific investigations. This year, less than 14% of all ERC Starting Grant applicants across all scientific disciplines received the award, with only 17 awardees in Computer Science across all of Europe and Israel!

These grants carry substantial research funding -- each winner receives up to 1.5 Million Euros over a period of 5 years to carry out their research. You can find more information about 2022 ERC Starting Grants here: https://erc.europa.eu/news-events/news/starting-grants-2022-call-results

The FINABIS Project

A fundamental question in computing is: What can programs find out algorithmically about other programs? If we want to analyze arbitrary programs, the answer is long known and simple: Essentially nothing. However, in recent decades, we have seen that if we restrict the class of analyzed programs, there is a rich variety of approaches to checking various important properties.

Understanding how to restrict the analyzed programs (while retaining as much expressivity as possible) has gained practical importance in the area of software verification. Here, algorithms for analyzing programs can be used to automatically check their correctness.

The available approaches to analyze programs typically transform a given program into an abstract model of computation. To account for program behaviors for all possible inputs, this usually results in models with infinitely many states. Designing algorithms that can work with such infinite-state systems poses a challenge. For example, we still do not have a clear picture of which types of infinite state spaces permit checking simple safety properties. In formal terms: For which infinite-state systems is reachability decidable?

In the FINABIS project ("Finite-state abstractions of infinite-state systems"), we are studying ways to transform infinite-state systems into finite-state systems that preserve some pertinent aspects of the original system. Understanding such transformations helps in two ways: First, finite-state systems are easier to work with algorithmically. So if our transformation preserves enough of the original system's behavior, we can simply analyze the finite system instead. Second, the specific transformations we study (subword closures and separability problems), and how we study them, are closely connected to understanding the decidability and complexity of reachability and also several other long-standing open problems in theoretical computer science.

MPI-SWS researcher Edon Kelmendi has received a Distinguished Paper award at the 2022 ACM/IEEE 37th Annual Symposium on Logic in Computer Science (LICS 2022) for his paper Computing the Density of the Positivity Set for Linear Recurrence Sequences.

Distinguished Paper awards are given to about 10% of papers at LICS. These are papers that, in the view of the LICS program committee, make exceptionally strong contribution to the field and should be read by a broad audience due their relevance, originality, significance and clarity.

MPI-SWS faculty member Rupak Majumdar has received the 2022 CONCUR Test-of-Time Award for his CONCUR 2003 paper on The Element of Surprise in Timed Games. The work was done in collaboration with Luca de Alfaro, Marco Faella, Thomas A. Henzinger, and Mariëlle Stoelinga.

The award citation reads as follows: "The paper studies concurrent two-player games played on timed game structures, and in particular the ones arising from playing on timed automata. A key contribution of the paper is the definition of an elegant timed game model, allowing both the representation of moves that can take the opponent by surprise as they are played "faster", and the definition of natural concepts of winning conditions for the two players -- ensuring that players can win only by playing according to a physically meaningful strategy. This approach provides a clean answer to the problem of time convergence, and the responsibility of the players in it. For this reason, it has since been the basis of numerous works on timed games. The algorithm established in the paper to study omega-regular conditions in this neat model of timed games is also enticing, resorting to mu-calculus on a cleverly enriched structure."

Sandra Kiefer has joined MPI-SWS as a research group leader, effective April 1, 2022. Her research interests include algorithmic and structural graph theory as well as logic in computer science, with a recent focus on the applicability of tools from these areas to the study of biochemical networks.

Sandra obtained her Ph.D. from RWTH Aachen University. For her work on combinatorial and logical approaches to graph comparison, she received the Ackermann Award 2020, the EACSL Outstanding Dissertation Award for Logic in Computer Science. After her Ph.D. studies, Sandra was a postdoctoral researcher at RWTH and at the University of Warsaw. She holds Bachelor’s degrees in Bioinformatics and Mathematics and a Master’s degree in Mathematics from Goethe University Frankfurt. She has also completed an M.Ed. degree in Mathematics and Spanish.

MPI-SWS scientific director Joël Ouaknine was appointed as a Fellow by the Association for Computing Machinery (ACM), the largest computer science association in the world, Joel, who leads the “Foundations of Algorithmic Verification” research group, was appointed ACM fellow for his contributions to algorithmic analysis of dynamical systems.

ACM has also elected as Fellows two researchers from our neighboring Max Planck Institute for Informatics: Thomas Lengauer is recognized for contributions to bioinformatics and medical informatics and Bernt Schiele is recognized for contributions to large-scale object recognition, human detection, and pose estimation.

The ACM Fellows program recognizes the 1% of ACM members who have made the most outstanding achievements in the field of computer and information technology. Worldwide 71 new ACM Fellows were elected this year, twelve of them in Europe, four in Germany and three of them in Saarbrücken.

Further Information: 

• https://www.acm.org/media-center/2022/january/fellows-2021


• https://awards.acm.org/fellows/award-winners


• https://www.mpi-sws.org/people/joel/

Joël Ouaknine, along with his co-authors James Worrell and Florian Luca, has received a Distinguished Paper award at the 2021 ACM/IEEE 36th Annual Symposium on Logic in Computer Science (LICS 2021) for his paper Universal Skolem Sets.

Distinguished Paper awards are given to about 10% of papers at LICS. These are papers that, in the view of the LICS program committee, make exceptionally strong contribution to the field and should be read by a broad audience due their relevance, originality, significance and clarity.

 

The third Salomaa prize has been awarded to MPI-SWS director Joël Ouaknine and James Worrell (Professor of Computer Science at Oxford University), for their outstanding contribution to Theoretical Computer Science, in particular to the theory of timed automata and to the analysis of dynamical systems.

The Salomaa prize in Automata Theory, Formal Languages and Related Topics is awarded each year by the Developments in Language Theory (DLT) Symposium. It was named to honour the scientific achievements and influence of Arto Salomaa, a founder of the DLT symposium. The prize consists of 2000 euros, funded by the University of Turku, Finland, the home university of Arto Salomaa.

 

Anne-Kathrin Schmuck, a postdoctoral fellow in the Rigorous Software Engineering group, was accepted to the Emmy Noether Programme of the German Science Foundation (DFG). This grant programme is the most prestigious programme for early career researchers from the DFG. It provides funding for an independent research group for a period of six years.

Anne-Kathrin's group will be hosted at MPI-SWS in Kaiserslautern and will develop automated modular synthesis techniques for reliable Cyber-Physical System (CPS) design. Her work draws inspiration from both Control Theory and Computer Science and centers around Reactive Synthesis, Supervisory Control Theory and Abstraction-Based Controller Design.

Researchers from the Max Planck Institute for Software Systems (MPI-SWS), the Max Planck Institute for Informatics (MPI-INF), and the Max Planck Institute for Security and Privacy (MPI-SP) have coauthored 17 papers at the colocated LICS 2020 and ICALP 2020, two of the top conferences in theoretical computer science. LICS is the premier conference on logic in computer science and ICALP is the flagship conference of the European Association for Theoretical Computer Science.

MPI-SWS papers:

1. Invariants for Continuous Linear Dynamical Systems. Shaull Almagor, Edon Kelmendi, Joël Ouaknine and James Worrell. ICALP 2020, Track B. [ Video | Paper]


2. The complexity of bounded context switching with dynamic thread creation. Pascal Baumann, Rupak Majumdar, Ramanathan Thinniyam Srinivasan and Georg Zetzsche. ICALP 2020, Track B. [ Video | Paper ]


3. Extensions of ω-Regular Languages. Mikołaj Bojańczyk, Edon Kelmendi, Rafał Stefański and Georg Zetzsche. LICS 2020. [ Video | Paper ]


4. Rational subsets of Baumslag-Solitar groups. Michaël Cadilhac, Dmitry Chistikov and Georg Zetzsche. ICALP 2020, Track B. [ Video | Paper ]


5. On polynomial recursive sequences. Michaël Cadilhac, Filip Mazowiecki, Charles Paperman, Michał Pilipczuk and Géraud Sénizergues. ICALP 2020, Track B. [ Video | Paper ]


6. An Approach to Regular Separability in Vector Addition Systems. Wojciech Czerwiński and Georg Zetzsche. LICS 2020. [ Video | Paper ]


7. The complexity of knapsack problems in wreath products. Michael Figelius, Moses Ganardi, Markus Lohrey and Georg Zetzsche. ICALP 2020, Track B. [ Video | Paper ]


8. The Complexity of Verifying Loop-free Programs as Differentially Private. Marco Gaboardi, Kobbi Nissim and David Purser. ICALP 2020, Track B. [ Video | Paper ]


9. On Decidability of Time-bounded Reachability in CTMDPs. Rupak Majumdar, Mahmoud Salamati and Sadegh Soudjani. ICALP 2020, Track B. [ Video | Paper ]

MPI-INF papers:

1. Scheduling Lower Bounds via AND Subset Sum. Amir Abboud, Karl Bringmann, Danny Hermelin and Dvir Shabtay. ICALP 2020, Track A.  [ Video | Paper ]


2. Faster Minimization of Tardy Processing Time on a Single Machine. Karl Bringmann, Nick Fischer, Danny Hermelin, Dvir Shabtay and Philip Wellnitz. ICALP 2020, Track A. [ Video | Paper ]


3. Hitting Long Directed Cycles is Fixed-Parameter Tractable. Alexander Göke, Dániel Marx and Matthias Mnich. ICALP 2020, Track A. [ Video | Paper ]


4. A (2 + ε)-Factor Approximation Algorithm for Split Vertex Deletion. Daniel Lokshtanov, Pranabendu Misra, Fahad Panolan, Geevarghese Philip and Saket Saurabh. ICALP 2020, Track A. [ Video | Paper ]


5. Hypergraph Isomorphism for Groups with Restricted Composition Factors. Daniel Neuen. ICALP 2020, Track A. [ Video | Paper ]


6. Deterministic Sparse Fourier Transform with an l∞ Guarante. Yi Li and Vasileios Nakos. ICALP 2020, Track A. [ Video | Paper ]

MPI-SP papers:

1. Deciding Differential Privacy for Programs with Finite Inputs and Outputs. Gilles Barthe, Rohit Chadha, Vishal Jagannath, A. Prasad Sistla and Mahesh Viswanathan. LICS 2020. [ Video | Paper ]


2. Universal equivalence and majority on probabilistic programs over finite fields. Charlie Jacomme, Steve Kremer and Gilles Barthe. LICS 2020. [ Video | Paper ]

Software systems have become ubiquitous in our modern world and, consequently, so have bugs and glitches. While many software failures are harmless and often merely annoying, some can have catastrophic consequences. Just imagine the dire results of an autonomous car failing to stop at a red traffic light or a plane's control system becoming unresponsive during takeoff or landing.

In our research, we address these problems and develop intelligent tools that help engineers to build safe and reliable hardware, software, and cyber-physical systems. To this end, we employ a unique and promising strategy, which has recently also regained major attention in the artificial intelligence community: combining inductive techniques from the area of machine learning and deductive techniques from the area of mathematical logic (e.g., see the recent Dagstuhl seminar on "Logic and Learning", which was co-organized by one of our group members). Specifically, our research revolves around three topics, to which the remainder of this article is devoted: verification, synthesis, and formal specification languages.

Verification

Verification is an umbrella term referring to tools and techniques that formally prove that a given system satisfies its specification. In the context of software, a popular approach is deductive verification. The idea is easy to describe: first, the given program is augmented with annotations (typically loop invariants, pre-/post-conditions of method calls, and shape properties of data structures), which capture the developer's intent and facilitate the deductive reasoning in a later step; second, the program, together with its annotations, is translated into formulas in a suitable logic, called verification conditions; third, the verification conditions are checked for validity using automated theorem provers. Thanks to brilliant computer scientists, such as Edsger Dijkstra and Tony Hoare, as well as recent advances in constraint solving, the latter two steps can be (almost) entirely automated. However, the first step still remains a manual, error-prone task that requires significant training, experience, and ingenuity. In fact, this is one of the main obstacles preventing a widespread adaptation of formal verification in practice.

To also automate the challenging first step, we have developed a novel approach, called ICE learning [1], which intertwines inductive and deductive reasoning. The key idea is to pit a (deductive) program verifier against an (inductive) learning algorithm, whose goal is to infer suitable annotations from test-runs of the program and failed verification attempts. The actual learning proceeds in rounds. In each round, the learning algorithm proposes candidate annotations based on the data it has gathered so far. The program verifier then tries to prove the program correct using the proposed annotations. If the verification fails, the verifier reports data back to the learning algorithm explaining why the verification has failed. Based on this new information, the learning algorithm refines its conjecture and proceeds to the next round. The loop stops once the annotations are sufficient to prove the program correct.

ICE learning has proven to be a very powerful approach that allows fully automatic verification of a wide variety of programs, ranging from recursive and concurrent programs over numeric data types [1], to algorithms manipulating dynamically allocated data structures [2], to industry-size GPU kernels [3]. In addition, the principles underlying ICE learning can be lifted to other challenging verification tasks, such as the verification of parameterized systems [4] as well as—in ongoing research—to the verification of cyber-physical and AI-based systems. You might want to try a demo immediately in your browser.

Synthesis

Synthesis goes beyond verification and could be considered the holy grail of computer science. In contrast to checking whether a hand-crafted program meets its specification, the dream is to fully automatically generate software (or a circuit for that matter) from specifications in a correct-by-construction manner.

Although this dream is unrealistic in its whole generality, there exist various application domains in which automated synthesis techniques have been applied with great success. In our own research, for instance, we have developed techniques for synthesizing safety controllers for reactive, cyber-physical systems that have to interact with a complex–and perhaps only partially known–environment [5, 6]. Moreover, we have proposed a general framework for generating loop-free code from input-output examples and specifications written in first-order logic [7]. Similar to ICE learning, these methods combine inductive and deductive reasoning, thereby unveiling and exploiting synergies of modern machine learning algorithms and highly-optimized symbolic reasoning engines.

Formal Specification Languages

Both verification and synthesis rely on the ability to write correct formal specifications, which have to precisely capture the engineer’s intuitive understanding of the system in question. In practice, however, formalizing the requirements of a system is notoriously difficult, and it is well known that the use of standard formalisms such as temporal logics requires a level of sophistication that many users might never develop.

We have recently started a new research project to combat this serious obstacle. Its main objective is to design algorithms that learn formal specifications in interaction with human engineers. As a first step towards this goal, we have developed a learning algorithm for the specification language “Linear Temporal Logic (LTL)”, which is the de facto standard in many verification and synthesis applications. You might think of this algorithm as a recommender system for formal specifications: the human engineer provides examples of the desired and undesired behavior of the system in question, while the recommender generates a series of LTL specifications that are consistent with the given examples; the engineer can then either chose one of the generated specifications or provide additional examples and rerun the recommender.

In ongoing research, we are extending our learning algorithm to a wide range of other specification languages, including Computational Tree Logic, Signal Temporal Logic, and the Property Specification Language. Moreover, we are developing feedback mechanisms that allow for a tighter integration of the human engineer into the loop. Again, you can try our technology immediately in your browser.

References

[1] D’Souza, Deepak; Ezudheen, P.; Garg, Pranav; Madhusudan, P.; Neider, Daniel: Horn-ICE Learning for Synthesizing Invariants and Contracts. In: Proceedings of the ACM on Programming Languages (PACMPL), volume 2 issue OOPSLA, pages 131:1–131:25. ACM, 2018.

[2] Neider, Daniel; Madhusudan, P.; Garg, Pranav; Saha, Shambwaditya; Park, Daejun: Invariant Synthesis for Incomplete Verification Engines. In: 24th International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2018), volume 10805 of Lecture Notes in Computer Science, pages 232–250. Springer, 2018

[3] Neider, Daniel; Saha, Shambwaditya; Garg, Pranav; Madhusudan, P.: Sorcar: Property-Driven Algorithms for Learning Conjunctive Invariants. In: 26th International Static Analysis Symposium (SAS 2019), volume 11822 of Lecture Notes in Computer Science, pages 323–346. Springer, 2019

[4] Neider, Daniel; Jansen, Nils: Regular Model Checking Using Solver Technologies and Automata Learning. In: 5th International NASA Formal Method Symposium (NFM 2013), volume 7871 of Lecture Notes in Computer Science, pages 16–31. Springer, 2013

[5] Neider, Daniel; Topcu, Ufuk: An Automaton Learning Approach to Solving Safety Games over Infinite Graphs. In: 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2016), volume 9636 of Lecture Notes in Computer Science, pages 204–221. Springer, 2016

[6] Neider, Daniel; Markgraf, Oliver: Learning-based Synthesis of Safety Controllers. In: 2019 International Conference on Formal Methods in Computer Aided Design (FMCAD 2019), pages 120–128. IEEE, 2019

[7] Neider, Daniel; Saha, Shambwaditya; Madhusudan, P.: Synthesizing Piece-wise Functions by Learning Classifiers. In: 22nd International Conference on Tools and Algorithms for the Construction and Analysis of Systems (TACAS 2016), volume 9636 of Lecture Notes in Computer Science, pages 186–203. Springer, 2016

[8] Neider, Daniel; Gavran, Ivan: Learning Linear Temporal Properties. In: 2018 International Conference on Formal Methods in Computer Aided Design (FMCAD 2018), pages 148–157. IEEE, 2018

Filip Mazowiecki is joining us from the University of Bordeaux, where he spent the last two years as a postdoc. His research area is formal verification, the study of verifying correct functioning of systems. He is mostly interested in the theoretical analysis of models like Petri nets and weighted automata, working on fundamental questions like reachability and equivalence.

Filip obtained his PhD at the University of Warsaw on the topic of database theory. After he obtained his PhD he switched to the area of formal verification, spending almost four years as a postdoc at the Universities of Warwick, Oxford and Bordeaux.

Georg Zetzsche has joined the institute as a tenure-track faculty member, effective November 1, 2018. He is joining us from the Institut de Recherche en Informatique Fondamentale (IRIF) at Université Paris-Diderot, where he has been a postdoctoral researcher. Georg's goal is to understand which questions about program behaviors and other infinite structures can be answered efficiently.  His research focuses on issues of decidability, complexity, synthesis, and expressiveness arising in program verification and mathematics.

Georg was previously a postdoctoral researcher in the Laboratoire Spécification et Vérification (LSV) at ENS Paris-Saclay. He obtained his PhD from the University of Kaiserslautern and his Diplom degree from Universität Hamburg. For his PhD work, Georg received the EATCS Distinguished Dissertation Award.

In 1937, a young Englishman by the name of Alan M. Turing published a paper with the obscure title "On computable numbers, with an application to the Entscheidungsproblem'' in the Proceedings of the London Mathematical Society. In doing so, he arguably laid the mathematical foundations of modern computer science. Turing's seminal contribution was to show that the famous Entscheidungsproblem, formulated by the great German mathematician David Hilbert several years earlier, could not be solved: more precisely, Turing proved (in modern parlance) that the problem of determining whether a given computer program halts could not be done algorithmically---in other words that the famous Halting Problem is undecidable.

Although seemingly at the time a rather esoteric concern, the Halting Problem (and related questions) have dramatically gained in importance and relevance in more contemporary times. Fast forward to the 21st Century: nowadays, it is widely acknowledged that enabling engineers, programmers, and researchers to automatically verify and certify the correctness of the computer systems that they design is one of the Grand Challenges of computer science. In increasingly many instances, it is absolutely critical that the software governing various aspects of our daily lives (such as that running on an aircraft controller, for example) behave exactly as intended, lest catastrophic consequences ensue.

What classes of infinite-state programs can be analyzed algorithmically?

Researchers at the Foundations of Algorithmic Verification group are investigating what classes of infinite-state programs can, at least in principle, be fully handled and analyzed algorithmically by viewing computer programs abstractly as dynamical systems, and they seek to design exact algorithms enabling one to fully analyse the behaviour of such systems. In particular, they are presently tackling a range of central algorithmic problems from verification, synthesis, performance, and control for linear dynamical systems, drawing among others on tools from number theory, Diophantine geometry, and algebraic geometry, with the overarching goal of offering a systematic exact computational treatment of various important classes of dynamical systems and other fundamental models used in mathematics, computer science, and the quantitative sciences. Some of their achievements include several decidability and hardness results for linear recurrence sequences, which can be used to model simple loops in computer programs, answering a number of longstanding open questions in the mathematics and computer science literature.

In a series of recent papers [1, 2],  they have attacked the so-called Zero Problem for linear differential equations, i.e., the question of determining algorithmically whether the unique solution to a given linear differential equation has a zero or not. Such equations, which go back as far as Newton, are ubiquitous in mathematics, physics, and engineering; they are also particularly useful to model cyber-physical systems, i.e., digital systems that evolve in and interact with a continuous environment. In their work, they obtained several important partial results: if one is interested in the existence of a zero over a bounded time interval, then it is possible to determine this algorithmically, provided that a certain hypothesis from the mathematical field of number theory, known as Schanuel's Conjecture, is true. They were also able to partially account for the fact that the Zero Problem has hitherto remained open in full generality: indeed, if one were able to solve it in dimension 9 (or higher), then in turn this would enable one to solve various longstanding hard open problems from a field of mathematics known as Diophantine approximation. In doing so, they therefore exhibited surprising and unexpected connections between the modelling and analysis of cyber-physical systems and seemingly completely unrelated deep mathematical theories dealing with questions about whole numbers.

References

[1] Ventsislav Chonev, Joel Ouaknine, and James Worrell. On recurrent reachability for continuous linear dynamical systems. In Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), 2016.

[2] Ventsislav Chonev, Joel Ouaknine, and James Worrell. On the Skolem Problem for continuous linear dynamical systems. In Proceedings of the 43rd International Colloquium on Automata, Languages, and Programming (ICALP), 2016.

Amaury Pouly, a postdoc in Joël Ouaknine's Foundations of Automatic Verification Group, has received the 2017 Ackermann Award for his PhD thesis, “Continuous-time computation models: From computability to computational complexity.” The Ackermann Award is an international prize presented annually to the author of an exceptional doctoral dissertation in the field of Computer Science Logic.

Amaury Pouly's thesis shows that problems which can be solved with a computer in a reasonable amount of time (more specifically problems which belong to the class P of the famous open problem “P = NP?”) can be characterized as polynomial length solutions of polynomial differential equations. This result paves the way for reformulating certain questions and concepts of theoretical computer science in terms of ordinary polynomial differential equations. It also revisits analog computational models and demonstrates that analog and digital computers actually have the same computing power, both in terms of what they can calculate (computability) and what they can solve in reasonable (polynomial) time.

Rupak Majumdar joins the institute's faculty as a scientific director. Rupak's research interests are in computer-aided verification and control of reactive, real-time, hybrid, and probabilistic systems; software verification and programming languages; and logic and automata theory.

Rupak's research spans the spectrum of formal verification techniques, ranging from theoretical foundations of logic and automata theory to practical software engineering tools that systematically analyze thousands of lines of code for programmer errors. In the field of software model checking, Rupak has made major contributions. Rupak, along with Ranjit Jhala, wrote the the model checker Blast, which is able to analyze over 100,000 lines of code for complex temporal properties. This achievement was a major milestone and proof of feasibility in the field of software verification and led to a flurry of academic and industrial activity in the area.

Rupak joins MPI-SWS from the University of California, Los Angeles, where he was on the faculty of the computer science department. Prior to that, Rupak received his Ph.D. degree in Computer Science from the University of California at Berkeley, and his B.Tech. degree in Computer Science from the Indian Institute of Technology at Kanpur.