Discrete Event Systems (HS 2020)
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 and German
Attention: The Lecture and Exercises will both be held via Zoom. The links to join the Zoom meetings have been distributed via email before the first lecture. In case you have not received any emails from the course organizers so far (e.g. in case of a late registration), please contact Béni Egressy.
|26.11.2020||Exercise 10, Question 3: Roger's candidates can be assumed to have unique ratings|
|17.12.2020||This year's exam will take place on Tuesday, February 9, 9:00am - 11:00am|
|16.10.2020||Finalized contents for the first part of the course (given by Prof. Vanbever), thank you all for participating! Special thanks to Angéline Pouget for providing an extensive sample solution for the bonus tasks in exercise session 5!|
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 two 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.
Regarding the first part of the course (given by Prof. Vanbever), the part on Turing machines (including "P vs NP") is not relevant for the exam.
If you would like some more exercises, you can also have a look at older exams (some with solutions): HS 2019, HS 2018, HS 2017, HS 2016, HS 2015, HS 2014, HS 2012, HS 2011, HS 2010, HS 2009, HS 2008 or HS 2007.
Please keep in mind that the content of the lecture has been updated a few times in recent years! Thus, some of the material from the old exams might no longer be covered in the current lecture and additional material has been added.
Dimitri Bertsekas, Robert Gallager.
Prentice Hall, 1991, ISBN: 0132009161
Online Computation and Competitive Analysis
Allan Borodin, Ran El-Yaniv.
Cambridge University Press, 1998
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
Introduction to Discrete Event Systems
Christos Cassandras, Stephane Lafortune.
Kluwer Academic Publishers, 1999, ISBN 0-7923-8609-4
Exorciser - Interaktive Lernsoftware für theoretische Informatik
Online Algorithms: The State of the Art
A. Fiat and G. Woeginger.
Approximation Algorithms for NP-hard Problems (Chapter 13 by S. Irani, A. Karlin)
Petri Nets: Properties, Analysis and Applications
Proceedings of the IEEE, vol. 99, issue 4, April 1989. pp. 541--580
Diskrete Strukturen (Band 2: Wahrscheinlichkeitstheorie und Statistik)
T. Schickinger, A. Steger.
Springer, Berlin, 2001
Introduction to the Theory of Computation
PWS Publishing Company, 1996, ISBN 053494728X