Course: Advanced Automata Theory

Summer 2017

Introduction

We shall study automata on finite/infinite words and trees and their relationship to logic and computer-aided verification of systems.

Computer science or math students with background in logic and theory of computation. (Familiarity with basic algorithms, logic, and theory of computation will be assumed). Talk to the instructor if you are not sure if you have the background. We shall try to keep the class self-contained, please attend the initial lecture for background material.

Further, I expect you (1) have "mathematical maturity" (e.g., you should be comfortable with proofs and abstract reasoning); (2) are interested in the material; and (3) are willing to spend time outside of class in order to better understand the material presented in lectures.

Grading will be based on a written, open-notes, final exam. Open notes means that you are free to bring your notes to the exam. However, you may not use internet access on any device during an exam.

In order to appear for the exam, you have to turn in homework problems (to be assigned approximately biweekly), write up lecture notes for two lectures, and present a result to the class.

The following text books cover most of the material (and much more):

  1. Michael Sipser, Introduction to the theory of computation, MIT Press

  2. Javier Esparza, Automata Theory Lecture Notes

  3. Erich Graedel, Wolfgang Thomas, Thomas Wilke, Automata, Logics, and Infinite Games, Springer

  4. Jeffrey Shallit, A Second Course in Formal Languages and Automata Theory, Cambridge University Press

In addition, we shall provide lecture notes, surveys, or research papers for topics not covered in these books.

Homework exercises will be handed out approximately every two weeks (weekday TBA). Your answers must be handed in until the day specified in the homework, at the beginning of the lecture.

Students may collaborate on homework assignments, but each student needs to individually write up a solution set and be prepared to present it in class on the due date. The work you submit in this course must be the result of your individual effort. You may discuss homework problems and general proof strategies or algorithms with other students in the course, but you must not collaborate in the detailed development or actual writing of problem sets. This implies that one student should never have in his or her possession a copy of all or part of another student's homework. It is your responsibility to protect your work from unauthorized access. In writing up your homework you are allowed to use any book, paper, or published material. However, you are not allowed to ask others for specific solutions, either in person or by using electronic forums such as newsgroups. Of course, during the administration of exams any form of cooperation or help is forbidden. Academic dishonesty has no place in a university; it wastes our time and yours, and it is unfair to the majority of students. Any dishonest behavior will be severely penalized and may lead to failure in the course.

Announcements

Lecture Notes

We hope to collaboratively create Wiki-like lecture notes at https://sandstorm.init.mpg.de/shared/fE1Q2Y28_shn-nE9vet1m_xlHI2hUKjdbzlSrYEpX9c

You can find a LaTeX tutorial online, which explains basics and first steps of writing LaTeX documents. Please also consult l2tabu, which is a list of do's and don't for writing LaTeX documents. The comprehensive LaTeX symbol list and the detexify website are useful, too (please contact me prior to importing or changing fonts to make particular symbol work).

Schedule

This schedule is preliminary and subject to change.

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Date

Course topic / lecture

Homework

Additional Materials (lecture notes/papers)

L1

April 18

Introduction to the course. Review of finite automata. Basic constructions.

http://www.jflap.org/

L2

April 19

Further constructions on finite automata. Regular expressions.

HW1

Reading: Sipser

L3

April 25

Review of complexity classes, decision problems on automata

L4

April 26

(Weak) monadic second order logics on words (WS1S). Buchi-Elgot theorem.

Reading: MukundNotes Advanced Reading: Graedel-Thomas-Wilke Ch 12

L5

May 02

Automata minimization: Homomorphisms.

HW2

Partition refinement algorithm / Marking algorithm

L6

May 03

Myhill-Nerode theorem.

L7

May 09

Minimization of DFAs.

L8

May 10

Bisimulation. Reduction of NFAs.

L9

May 16

Learning from examples. Passive learning.

HW3

RPNI Algorithm

L10

May 17

Angluin's Algorithm (L*). libalf.

Angluin's Algorithm

L11

May 23

Omega automata: Buchi, co-Buchi, Rabin, Streett.

Reading: BuchiAutomata

L12