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

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

    c. 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

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.

L2

April 19

Review of complexity classes. Further constructions on finite automata.

L3

April 25

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

L4

April 26

Antichains. Transducers. Alternating automata.

L5

May 02

Automata minimization: Myhill-Nerode theorem, non-determinism.

L6

May 03

Automata learning: Passive learning, L*.

L7

May 09

Applications of finite automata and learning. libalf.

L8

May 10

Spill slot.

L9

May 16

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

L10

May 17

Conversions between automata. Deterministic and non-deterministic automata.

L11

May 23

MSO (S1S) and Buchi's theorem.

L12

May 24

Determinization of automata.

L13

May 30

Determinization of automata.

L14

May 31

Alternating omega-automata: Miyano and Hayashi's construction.

L15

June 06

Linear temporal logic. Automata-theoretic model checking.

L16

June 07

Overflow: Applications, tools, open problems.

L17

June 13

Church's problem. Realizability. Games and synthesis.

L18

June 14

Safety, reachability, Buchi, parity games.

L19

June 20

Parity games and mu-calculus.

L20

June 21

Bounded synthesis.

L21

July 04

Tree automata and decidability of S2S

L22

July 05

Beyond regularity: nested word automata.

L23

July 11

Context free languages. Parikh's theorem.

L24

July 12

Timed automata.

L25

July 18

TBD.

L26

July 19

TBD.