Course: CS280 Advanced Automata Theory

Winter 2006

• Instructor: Rupak Majumdar (Email: rupak@cs.ucla.edu)
• Lectures: Monday, Wednesday 4:00-5:30 Location 166 Royce
• Office Hours: After class on Wednesdays

General Information

• Syllabus and contents. We shall study automata on infinite words and trees and their relationship to logic and computer-aided verification of systems. List of Topics
• Intended Audience. Computer science or math graduate students with background in logic and theory of computation. (Familiarity with CS181 will be assumed). Talk to the instructor if you are not sure if you have the background.
• Grading. Grading will be based on homework problems (to be assigned approximately biweekly), paper presentations, and a final project. In addition, students will be expected to scribe some lecture notes in latex (Use this template).

• Lecture 1. Administration. Automata on finite words. Word models. Lecture Notes
  References:
  • W. Thomas. Languages, automata, and logic.
  • M. Sipser. Introduction to the theory of computation, 2nd Edition. Course Technology, 2005.
• Lecture 2. Monadic second order logic on words. Buchi-Elgot Theorem. Lecture Notes
• Lecture 3. Alternating automata on finite words. Buchi automata and omega-regular languages. Lecture Notes
  References:
  • W. Thomas. Automata on infinite objects. Handbook of Theoretical Computer Science, vol B. Elsevier.
  • M. Mukund. Finite state automata on infinite inputs.
  • O. Kupferman and M. Vardi. Weak alternating automata are not that weak. A second complementation construction.
• Lecture 4. Different acceptance criteria. Decidability of S1S. Complementation.
  Lecture Notes
• Lecture 5. Towards Safra's construction.
• Lecture 6. Safra's construction. Alternating Buchi automata and Miyano-Hayashi construction.
• Lecture 7. Kupferman and Vardi's construction. Properties of runs of ACW.
• Lecture 8. LTL as the first order fragment of S1S. LTL model checking and satisfiability through the tableau construction. LTL -> ABW -> NBW.
  Moshe Vardi, An automata theoretic approach to linear temporal logic.
• Lecture 9,10. Automata on infinite trees. Games on graphs.
  W. Zielonka. Infinite games on finitely colored graphs with applications to automata on infinite trees.
• Lecture 11, 12. Parity games. Rabin's complementation theorem.
  Marcin Jurdzinski, Mike Paterson, and Uri Zwick. A Deterministic Subexponential Algorithm for Solving Parity Games. Proceedings of ACM-SIAM Symposium on Discrete Algorithms, SODA 2006.
• Lecture 13,14. Muller tree automata to parity automata. Complementation. The mu-calculus. Mu-calculus model checking.
  Kupferman, Vardi, and Wolper. An automata theoretic approach to branching time model checking
  W. Thomas. On the synthesis of strategies in infinite games (gives the Muller to parity conversion, see also the Thomas survey mentioned above).
• Lecture 15. Matrix games. von Neumann's minmax theorem. Linear programming solutions.
  This material is accessible from any book on game theory. I shall use the book by Owen. Here is an interesting paper about the different proofs of th eminimax theorem by von Neumann.
• Lecture 16. Concurrent reachability games.
  L. de Alfaro and R. Majumdar. Quantitative solution of concurrent games.
  L. de Alfaro, T.A. Henzinger, and O. Kupferman. Concurrent reachability games.
• Lecture 17. Nash equilibria in matrix games.