Distributed Computing
ETH Zurich

Discrete Event Systems (HS 2021)

Over the past few decades the rapid evolution of computing, communication, and information technologies has brought about the proliferation of new dynamic systems. A significant part of activity in these systems is governed by operational rules designed by humans. The dynamics of these systems are characterized by asynchronous occurrences of discrete events, some controlled (e.g. hitting a keyboard key, sending a message), some not (e.g. spontaneous failure, packet loss).

The mathematical arsenal centered around differential equations that has been employed in systems engineering to model and study processes governed by the laws of nature is often inadequate or inappropriate for discrete event systems. The challenge is to develop new modeling frameworks, analysis techniques, design tools, testing methods, and optimization processes for this new generation of systems.

In this lecture we give an introduction to discrete event systems. We start out the course by exploring the limits of what is computable and what is not. In doing so, we will consider three distinct models of computation which are often used to model discrete event systems: finite automata, push-down automata and Turing machines (ranked in terms of expressiveness power). In the second part of the course we analyze discrete event systems. We first examine discrete event systems from an average-case perspective: we model discrete events as stochastic processes, and then apply continuous time markov chains and queueing theory for an understanding of the typical behavior of a system. Then we analyze discrete event systems from a worst-case perspective using the theory of online algorithms and adversarial queueing. In the last part of the course we introduce methods that allow to formally verify certain properties of Finite Automata and Petri Nets. These are some typical analysis questions we will look at: Do two given systems behave the same? Does a given system behave as intended? Does the system eventually enter a dangerous state?

Course language: English

Lecture by Dr. Romain Jacob, Prof. Laurent Vanbever, and Prof. Roger Wattenhofer, Thursday 14.15-16.00 @ HG D 7.2, starting 23.09.2021.

Exercises by Zhao Meng, Ye Wang, Tibor Schneider and Roland Schmid, Thursday 16.15-17.45 @ HG D 7.2.

Attention: Please note that you are required to wear a medical mask and present a valid Covid certificate to attend the lecture and/or the exercises. As an alternative, you may follow the lecture and exercises via a live stream provided by ETH Multimedia Services. Please note that you will not be able to ask any questions then.


01.10.2021We added a new task to train (step-by-step) de-randomization to Exercise 2, the NFA->GNFA->REX task has been moved to Exercise 3 instead.
14.10.2021Finalized contents for the first part of the course (given by Prof. Vanbever), thank you all for participating!

Exercise Proceedings

At the beginning of every lecture week, we will publish a new exercise sheet here. This exercise sheet is intended to be solved during the exercise session on Thursday where tutors will be available to assist you and to answer potential questions. The exercises often require information from the lecture notes, so please make sure that you have them available in some way.

You can hand in your solutions for correction after the exercise session on a voluntary basis. But this is not mandatory or required to be admitted to the exam.

Lecture Material

Chapter Title Lecturer Lecture Notes Exercises Responsible Assistant Additional Material
Chapter 0 Introduction
Laurent Vanbever PDF 1:1
PDF 4:1
--- --- ---
Chapter 1 Regular Languages
23.09.2021 – 30.09.2021
Laurent Vanbever PDF 1:1
PDF 4:1
Exercise 1
Solution 1
Slides 1

Exercise 2
Solution 2
Slides 2
Notes 2
Roland Schmid Blackboard content (23.09.2021)
Lecture 1 Recording (HS20)
Exercise 1 Recording (HS20)

Lecture 2 Introduction & Recap Slides
Lecture 2 Counter Example
Lecture 2 Recording (HS20)
Exercise 2 Recording (HS20)
Chapter 2 Non-Regular Languages
07.10.2021 – 14.10.2021
Roland Schmid,
Laurent Vanbever
PDF 1:1
PDF 4:1
Exercise 3
Solution 3
Slides 3
Notes 3

Exercise 4
Solutione 4
Slides 4
Notes 4
Roland Schmid Lecture 3 Introduction & Recap Slides
Lecture 3 Notes
Lecture 3 Recording (HS20)
Exercise 3 Recording (HS20)

Lecture 4 Introduction & Recap Slides
Lecture 4 Recording (HS20)
Exercise 4 Recording (HS20)
Example: Tandem-Pumping Lemma
Chapter 3 Markov Chains
Roger Wattenhofer PDF 1:1 Exercises
Zhao Meng Lecture Recording (HS20)
Exercise Recording (HS20)


Regarding the first part of the course (given by Prof. Vanbever), the slides on context-sensitive grammars and transducers are not relevant for the exam. Other than that, all material covered in the lecture and the exercises can be prospects for the examination as usual.

Old Exams

If you already think about the exam, or would like some more exercises, you can also have a look at older exams (some with solutions): HS 2020, HS 2019, HS 2018, HS 2017, HS 2016, HS 2015.

Please keep in mind that the content of the lecture has been updated a few times in recent years, especially the third part which is taught by a new lecturer! Thus, some of the material from the old exams might no longer be covered in the current lecture and additional material has been added.


[bertsekas] Data Networks
Dimitri Bertsekas, Robert Gallager.
Prentice Hall, 1991, ISBN: 0132009161
[borodin] Online Computation and Competitive Analysis
Allan Borodin, Ran El-Yaniv.
Cambridge University Press, 1998
[burch] Symbolic Model Checking
Burch, J. R. and Clarke, E. M. and McMillan, K. L. and Dill, D. L. and Hwang, L. J.
Inf. Comput. 98, 2 (June 1992), pp. 142-170
[cassandras] Introduction to Discrete Event Systems
Christos Cassandras, Stephane Lafortune.
Kluwer Academic Publishers, 1999, ISBN 0-7923-8609-4
[exorciser] Exorciser - Interaktive Lernsoftware für theoretische Informatik
[fiat] Online Algorithms: The State of the Art
A. Fiat and G. Woeginger.
[hochbaum] Approximation Algorithms for NP-hard Problems (Chapter 13 by S. Irani, A. Karlin)
D. Hochbaum.
[murata] Petri Nets: Properties, Analysis and Applications
Tadao Murata.
Proceedings of the IEEE, vol. 99, issue 4, April 1989. pp. 541--580
[schickinger] Diskrete Strukturen (Band 2: Wahrscheinlichkeitstheorie und Statistik)
T. Schickinger, A. Steger.
Springer, Berlin, 2001
[sipser] Introduction to the Theory of Computation
Michael Sipser.
PWS Publishing Company, 1996, ISBN 053494728X