Course

References

Lecture Notes

Problem Sets

AGV: Lecture Notes

• Lecture 1, Apr 12, 2011
  After some introductory remarks about verification and synthesis, we started with basic definitions about Büchi automata.
  
  Lecture Notes 1
  
  Summary Slides 1

• Lecture 2, Apr 19, 2011
  We defined omega-regular expressions and proved Büchi’s Characterization Theorem (1962): An omega-language is Büchi-recognizable iff it is omega-regular.
  
  Lecture Notes 2
  
  Summary Slides 2

• Lecture 3, Apr 26, 2011
  We studied deterministic Büchi automata and got started on the proof that the Büchi-recognizable languages are closed under complement. For this purpose, we introduced the concept of ranked run DAGs.
  
  Lecture Notes 3 (Notes updated on May 1, 2011)
  
  Summary Slides 3

• Lecture 4, May 3, 2011
  We completed the complementation construction and introduced Muller automata.
  
  Lecture Notes 4 (Notes updated on May 4, 2011)
  
  Summary Slides 4

• Lecture 5, May 10, 2011
  We started the proof of McNaughton’s Theorem: Every Büchi-recognizable language is recognizable by a deterministic Muller automaton.
  
  Lecture Notes 5 (Notes updated on May 12, 2011)
  
  Summary Slides 5

• Lecture 6, May 17, 2011
  After completing the proof of McNaughton’s Theorem, we started our discussion of logics over infinite sequences. We introduced linear-time temporal logic (LTL) and proved that the models of an LTL formula form a non-counting language.
  
  Lecture Notes 6
  
  Summary Slides 6

• Lecture 7, May 24, 2011
  We looked at three interesting logics over infinite sequences: Quantified Propositional Temporal Logic (QPTL), which is LTL extended by quantification over propositional variables, the second-order theory of 1 successor (S1S) and the weak second-order theory of 1 successor (WS1S). QPTL, S1S, WS1S, and Büchi automata are equally expressive, while LTL is strictly weaker.
  
  Lecture Notes 7 (Notes updated on June 27, 2011)
  
  Summary Slides 7 (Slides updated on June 13, 2011)

• Lecture 8, May 31, 2011
  We introduced alternating Büchi automata and translated LTL formulas to alternating automata.
  
  Lecture Notes 8 (Notes updated on June 6, 2011)
  
  Summary Slides 8

• Lecture 9, June 6, 2011
  We proved that alternating Büchi automata can be translated into equivalent nondeterministic Büchi automata (Miyano and Hayashi, 1984).
  
  Lecture Notes 9 (Notes updated on July 25, 2011)
  
  Summary Slides 9

• Lecture 10, June 13, 2011
  We proved memoryless determinacy for Reachability, Büchi, and parity games.
  
  Lecture Notes 10 (Notes updated on June 27, 2011)
  
  Summary Slides 10

• Lecture 11, June 21, 2011
  We introduced tree automata.
  
  Lecture Notes 11
  
  Summary Slides 11

• Lecture 12, June 28, 2011
  We proved that parity tree automata are closed under complement, and related tree automata to the monadic second-order theories with two, n, and ω successors.
  
  Lecture Notes 12 (Notes updated on July 9, 2011)
  
  Summary Slides 12

• Lecture 13, July 5, 2011
  We introduced CTL, CTL*, and the modal μ-calculus.
  
  Lecture Notes 13
  
  Summary Slides 13

• Lecture 14, July 12, 2011
  We introduced alternating tree automata and provided translations from CTL and the alternation-free μ-calculus to alternating Büchi tree automata.
  Lecture Notes 14 (Notes updated on July 25, 2011)
  
  Summary Slides 14

• Lecture 15, July 19, 2011
  We translated formulas of the full μ-calculus to alternating parity tree automata and wrapped up with a summary of the course’s main points.
  
  Lecture Notes 15