Timed and Hybrid Systems

Monday, 5:00-6:50 PM
Room 513, WWH
Amir Pnueli

Reaching Me

Amir Pnueli

Prerequisites: Some background in algorithm design, familiarity with the language of first-order logic, and parallel programs.

Course requirements: Assignments and a term project.

Recommended: Temporal Verification of Reactive Systems: Safety by Zohar Manna and Amir Pnueli, Springer-Verlag

Course Description

The class of computer systems whose modeling, analysis, and development are most challenging is the class of reactive systems. Reactive systems are systems whose role is to maintain an ongoing interaction with their environment rather than produce some final value upon termination. Typical examples of reactive systems are Network protocols, Air traffic control system, Programs controlling mechanical devices such as a train, a plane, or ongoing processes such as a nuclear reactor. Recently, there is an awakened interest in reactive systems due to the emergence of embedded systems as a major research field.

The Formal Methods approach to software analysis and construction is based on viewing a program and its execution as mathematical objects and applying mathematical and logical techniques to specify and analyze the properties and behavior of these objects. The main advantages of the formal approach to software construction is that, whenever applicable, it can lead to an increase of the reliability and correctness of the resulting programs by several orders of magnitude.

Several level of abstraction can be used in the study of reactive and embedded systems. At the highest level of abstraction, we only care about the temporal precedence of events and actions, and can guarantee that a system satisfies a requirement such as "every request is eventually followed by a response". However, at this level of modeling we cannot bound the response time by actual numbers. In the course, we consider two successive refinements of our modeling and specification abilities. The first refinement considers the model of real-time systems. In this model, we represent, specify, and analyze the temporal distance between events, thus being able to require and verify a property such as "every request is eventually followed by a response, which must occur within the time interval [3,5] from the request".

The next level of refinement considers the model of hybrid systems. In this model, we consider a system consisting of a combination of components some of which are discrete, such as programs, while the other are continuous, such as a motor driving a railroad gate barrier. This model employs discrete as well as continuous analysis tools in order to analyze and verify the correctness of hybrid systems, typically corresponding to a digital program controlling a continuous environment.

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Class Presentations


  • Reference Materials