Course description

This course provides an introduction to the state-of-the art techniques for verification of hybrid systems. Hybrid systems are systems exhibiting mixed discrete-continuous behaviors which typically arise when a digital computer is used to control physical entitites. Some of the application areas include Robotics, Automotives, Industrial Process Control, and Medical Devices. We will discuss some of the standard elements of automated verification, namely, model-checking, logical formalism for specifying properties, approximation techniques and deductive verification techniques in the context of hybrid systems.

Pre-requisite: Some knowledge of differential equations is necessary. A course in algorithms and/or theory of computation is helpful but not necessary.

Credits and grading:

Credits: 6 units
Requirements: Reading papers, participating in discussions
Grading: grading will be Pass/Fail

List of Topics

  1. Model-checking
    • Timed Automata: decidability of reachability.
      1. Rajeev Alur, David L. Dill: A Theory of Timed Automata.
      2. Patricia Bouyer: An Introduction to Timed Automata.
    • Other decidable classes and undecidability results.
      1. Thomas A. Henzinger, Peter W. Kopke, Anuj Puri, Pravin Varaiya: What's Decidable about Hybrid Automata?
  2. Timed temporal logics
    • Metric Temporal Logic, Timed Computation Tree Logic: Expressiveness and decidability
      1. Joel Ouaknine, James Worrell: On the decidability and complexity of Metric Temporal Logic over finite words.
      2. The benefits of relaxing punctuality. Rajeev Alur, Tomas Feder, Thomas A. Henzinger
      3. Model-Checing in Dense Real-Time. Rajeev Alur, Costas Courcoubetis, David Dill
  3. Abstraction techniques
    • Predicate abstraction, Counter-example guided abstraction refinement
      1. Rajeev Alur, Thao Dang, Franjo Ivancic: Counterexample-guided predicate abstraction of hybrid systems.
      2. Ashish Tiwari: Abstractions for hybrid systems. Formal Methods in System Design
    • Hybridization techniques, bounded-error approximation techniques
      1. Reachability of Uncertain Linear Systems Using Zonotopes. Antoine Girard
      2. Hybridization Methods for the Analysis of Non-Linear Systems. Eugene Asarin, Thao Dang, and Antoine Girard
  4. Deductive verification
    • Hybrid programs, differential dynamic logic
      1. Andre Platzer. Differential dynamic logic: Automated theorem proving for hybrid systems.
  5. Additional Topics depending on time: SAT/SMT solvers, Templates

Additional Resources:

  1. Verification and Control of Hybrid Systems: A Symbolic Approach. Paulo Tabuada. Springer, 2009.
  2. Logical Analysis of Hybrid Systems. Andre Platzer.
  3. Mathematical Logic. Joseph R. Shoenfield.