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Automata Theory

In the lecture about theoretical computer science you have seen finite automata, pushdown automata, and Turing machines. All three of them operate on finite words. However, there are other automata models and automata that do not operate on finite words but, e.g., on infinite words, on nested words, on trees, etc. In this seminar we will have a look at automata models that you have not seen in the lecture on theoretical computer science as well as on related topics.

Course type Seminar / Proseminar
Instructors Prof. Dr. Andreas Podelski, Dr. Matthias Heizmann, Alexander Nutz, Christian Schilling
Kick-off meeting
Thu, October 19, 13:00 s.t., building 052, room 00-016
Presentation language
English (Seminar) / German (Proseminar)
4 (Seminar) / 3 (Proseminar)
Course Catalog Advanced Topics in Automata Theory (Seminar)
Introduction to Automata Theory (Proseminar)


  • As the next step, you should send an email to Christian in which you choose at least three topics (possibly with priorities) and state your preferences for the talk dates (currently the tendency is to have a block seminar on Saturday, February 3). Please send this email until Sunday, October 29, 23:59. Note that we will add the information which topic is suited for proseminar/seminar only at the beginning of next week, so you may want to wait a bit.
  • We added the available topics (scroll down).
  • We fixed the kick-off meeting (see above).

Process of the seminar

  • You participate in the kick-off meeting, where we present the available topics. Feel free to hand in your favorite topic in advance.
  • You contact the instructors to obtain a topic. You may suggest a topic by yourself, pick one of the suggested topics, or find a topic suitable for you in a discussion with your supervisor.
  • You have a meeting with your supervisor in which we discuss relevant literature and develop a very coarse sketch of your talk (deadline: four weeks before your talk).
  • You write a proposal in which you explain what you are going to present in your talk, together with an abstract of your talk. You submit your abstract and your proposal via email to your supervisor (deadline: three weeks before your talk).
  • Your proposal is reviewed by your supervisor and two other participants.
  • You write two reviews about other participants' proposals and send them via email to the supervisor (deadline: one week after you received the proposal).
  • You receive reviews for your proposal (deadline: two weeks before your talk).
  • You submit your slides via email to your supervisor (deadline: one week before your talk).
  • You have a meeting with your supervisor in which you get feedback for your slides.
  • You give a talk of 30 minutes (Seminar) / 25 minutes (Proseminar).
  • You attend the talks of all other participants.

Proposals of the talk

The proposal should consist of around five pages in which you explain what you are going to present in your talk. The proposal may contain:

  • short overview for the reviewers (the reviewers will probably not know your topic)
  • structure of your talk
  • aspects of the topic that you present (why?) and ignore (why?)
  • examples occurring in the talk (why these examples? Is there a running example that can be used for demonstration?)
  • which definitions are presented formally? (why?), which definitions are just mentioned informally? (why?)
  • which notation is used? (why?)
  • which theorems are presented, which of them will be proven (why?), which proofs will be omitted (why?), will you use motivating examples in the proof?

Abstract of the talk

  • The abstract consists of one paragraph that summarizes what you present in the talk.
  • We will send an invitation for the seminar to all students and members of our chair. This invitation contains the abstracts of all talks.

The talk

  • The goal of your talk is that the audience (bachelor and master students, familiar with computer science in general, probably no experts in the topic) has the possibility to learn something new about an interesting topic. How well you achieved this goal will determine the grade of your talk.
  • In a seminar you have to show that you are able to present some topic to other people. You do not have to show how well you understood the topic for yourself. How well you understood the topic has no direct influence on your grade, but only how well you presented the topic to the audience.
  • You may use and copy any source of information (but do not forget to cite it). If you think your talk is just a "remix" of existing talks tailored to your audience, you might have done a great job. But do not let yourself be fooled by well-structured and fancy talks found in the web, each talk was prepared to a specific audience.
  • If you agree, we will put your slides on this web page. Keep in mind that if you have copied images in your slides this might not be possible anymore (copyright restrictions). Of course, it will not have any effect on your grade whether we may publish your slides or not.

Review of the proposal

  • Give a short summary of the talk based on the proposal (to detect misunderstandings right at the start).
  • Be generous with your criticism. It is very unlikely that a student will get a bad grade because you revealed some problems in his/her proposal. However, it is very likely that a student will get a better grade if he/she was able to resolve a problem in his/her talk, thanks to your review.
  • Give reasons for your criticism (e.g., "It is not possible to understand Lemma 2 because term foo was not explained.").  You are also allowed to give your personal opinions, if you do so mark them as such (e.g., "Theorem 1 is very difficult to understand, in my opinion you should give an example first.").
  • The following questions might be helpful to write your review
Is the proposal sufficiently well written to be readable?
Is the appearance and structure of the proposal appropriate?
Is the comprehensibility of the talk supported by relevant examples and figures?
Is the proposed structure of the talk sensible and balanced?
Are all propositions made by the author correct?
Is the line of reasoning concerning the presentation complete and accurate?
Has the author argued his/her case effectively?
Does the author use the common notation and terminology? Where would you suggest something different?
Is the schedule of the author sensible? Do you think the talk will fit into the time slot?


Your overall grade will be composed according to the following proportion.

  • 10% grade of your proposal
  • 20% grade of your reviews
  • 70% grade of your talk

Topics & literature

There is not a one-to-one correspondence between seminar talks and topics. Several students may give talks on the same topic, but present different aspects. The suggested literature should give you a first impression of the topics. We assign the exact literature in cooperation with you after you stated your preferences for the topic. More literature does not mean more reading, just more options. The order of appearance is arbitrary.

If requested, some topics may also be presented in groups of two.

Some of the papers are only available via the network of our university (e.g., via vpn). If you have some problem accessing the papers, please ask us.


Literature: Wikipedia, CAV '06, TACAS '10, TACAS '10

Boolean finite automata

Literature: arXiv '17

Büchi automata

Literature: Automata theory - An algorithmic approach (Chapter 11 Section 1-2), Automata on infinite objects (Chapter I Section 1-2)

Büchi automata complementation

Literature: LMCS '07

Complexity: NP's structure

Literature: Computers and intractability - A guide to the theory of NP-completeness (Chapter 7.1)

Complexity of Büchi automata minimization

Literature: arXiv '10

Complexity of games

Literature: PushPush and Push-1 are NP-hard in 2D, Classic Nintendo games are (NP-)hard, Gaming Is a hard job, but someone has to do it!, Playing games with algorithms: algorithmic combinatorial game theory, The hardness of the Lemmings game, or Oh no, more NP-completeness proofs, Computational complexity of two-dimensional platform games, Lemmings is PSPACE-complete

Complexity of visibly pushdown language emptiness

Literature: Inf. Process. Lett. '11

Context-sensitive languages

Literature: Wikipedia, Formal languages (Chapter 5), SIAM J. Comput. '88, MFCS '01

DFA families

Literature: MFCS '16

Efficient representation of finite sets

Literature: Automata theory - An algorithmic approach (Chapter 7), RAMICS '12

Minimization of tree automata

Literature: TACAS '16

MSO logic & finite automata

Literature: Automata theory - An algorithmic approach (Chapter 9), POPL '17

Number theory & automata

Literature: arXiv '17, arXiv '17

Petri nets

Literature: Applied Automata Theory (Chapter 6), FMSD '02, Software & Systems Modeling '14

Reversible finite automata

Literature: DLT '15

Set automata

Literature: DLT '14 [technical report], DCFS '14, DLT '17


Literature: SIAM J. Comput. '05

State complexity

Literature: CIAA '12

Tree automata

Literature: Tree automata - Techniques and applications

Visibly pushdown automata

Literature: Wikipedia, STOC '04, J ACM '09
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