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Cyber-Physical Systems I - Discrete Models

In this course we demonstrate how cyber-physical systems, in the wide range of their heterogeneous aspects (large-scale systems, system of systems, embedded systems, concurrent systems, hardware systems, software systems) can be modeled using the basic notion of transition systems. We consider relevant formalisms for modeling correctness properties of cyber-physical systems, and show how the models can be analyzed using algorithmic methods in order to prove correctness or find errors.

Course type Lecture
Instructors Prof. Dr. Andreas Podelski, Elisabeth HenkelDominik Klumpp

Wednesday 16:00 - 18:00, building 101, room SR 01-009/13
Lecture materials and recordings will be uploaded to ILIAS.


Weekly exercise groups (in person) -- starting on October 16th/17th

Group 1: Monday, 14:00 - 16:00, SR 00-014, building 078
Group 2: Monday, 16:00 - 18:00, SR 01-009/13, building 101
Group 3: Tuesday, 16:00 - 18:00, SR 00-007, building 106

Language of instruction English
Credits 6
Exams Written exam
Course catalog Cyber-Physical Systems -- Discrete Models - Lecture
Cyber-Physical Systems -- Discrete Models - Exercises
ILIAS course

Cyber-Physical Systems I - Discrete Models WS23/24
If you are registered on HisInOne but do not have access to this course, send an email to Elisabeth Henkel (see above).


The lecture is planned as an in-person course.


  • Oct 16: Link to Ilias added. Links to deprecated resources removed.
  • Oct 05: Note that the exercise sessions will start already on 16th and 17th October. The first lecture is on 18th October.
  • Oct 05: Homepage online.


The course provides an introduction to discrete models of cyber-physical systems, their analysis and verification:

  • The students learn how to model cyber-physical systems as transition systems. Here, the main focus lies on software and hardware aspects of cyber-physical systems and on methods for modelling parallelism and communication.
  • Moreover, the students learn how to express properties about such systems. The course covers different mechanisms to specify temporal properties including linear time properties and branching time properties such as LTL, CTL, and CTL* properties.
  • Finally, the course demonstrates how to develop algorithms for checking whether these properties hold. After presenting algorithms for explicit state systems, we introduce symbolic BDD-based algorithms which are able to tackle the well-known "state explosion problem". In addition, the course covers basic "Bounded Model Checking" (BMC) techniques, which restrict the analysis to computation paths up to a certain length and reduce the verification problem to a Boolean satisfiability problem.


There will be one (in-person) lecture each week, Wednesday 16:00 - 18:00.

We will upload the slides and lecture recordings in ILIAS.


The lecture is accompanied by weekly exercises. Each Thursday, we will publish an exercise sheet. Students will have time until the next Wednesday to prepare solutions for the problems stated on the exercise sheet. Solutions may be submitted alone or in groups of two. The solutions must be submitted by 15:59 on Wednesday via the lecture's ILIAS course. The tutors will mark the solutions and discuss them in the exercise groups the following week.

The exercises are not optional. You must obtain at least 50% of the exercise points. The idea is that you train yourself to write down things in a formally correct way. Your solutions to the exercises will help us to evaluate your knowledge and to evaluate your capability to solve the exercises in the exam.

The students present their solutions in the exercise group. This is done on a voluntary basis (you can choose which exercises you want to present), but every student must present his/her solution to an exercise in an exercise group at least once in the semester.

Exercise groups will meet in-person at the TF campus. You can find the times of the exercise groups in the table above. Please register for your exercise group in HisInOne.

The exercise sessions will NOT be recorded. No solution for the exercises will be uploaded. We encourage you to actively participate in the exercise sessions, as they are essential to practice and better understand the lecture content.


There will be a written exam. Further details will be announced later.

You may bring one DIN A4 sheet to the exam. Both sides of this sheet may be filled with any notes (e.g., definitions, theorems, examples) but the notes have to be handwritten. You must not use any other material in the exam (except for writing utensils).



The lecture slides will be uploaded to the lecture's ILIAS course.

Exercise Sheets

The weekly exercise sheets will be uploaded to the lecture's ILIAS course. You can submit your solution via ILIAS (within your respective exercise group).

Old lectures

You can find information on previous courses on the following web pages.


The lecture will follow very closely the famous textbook "Principles of Model Checking" by Christel Baier and Joost-Pieter Katoen (MIT Press).  A copy is available in the library.