AGV: Lecture Notes
- Lecture 1, Oct 23, 2012.
As motivation & overview for the course, we looked at temporal logics along the linear/branching-time spectrum and their relationship to automata and games.
Lecture Notes 1 (updated on Oct 27, 2012)
- Lecture 2, Oct 25, 2012.
We introduced Büchi automata and omega-regular expressions and proved the closure properties of the Büchi-recognizable languages needed for Büchi’s Characterization Theorem (1962): An omega-language is Büchi-recognizable iff it is omega-regular.
Intro Slides 2, Lecture Notes 2 (updated on Oct 27, 2012)
- Lecture 3, Oct 30, 2012.
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.
Intro Slides 3, Lecture Notes 3
- Lecture 5, Nov 13, 2012
We introduced Muller automata and got started on the proof of McNaughton’s Theorem: Every Büchi-recognizable language is recognizable by a deterministic Muller automaton.
Intro Slides 5, Lecture Notes 5 (updated on Nov 28, 2012)
- Lecture 6, Nov 20, 2012
Proving McNaughton’s Theorem, we studied the transformation of nondeterministic Büchi automata into semi-deterministic Büchi automata, and the transformation of semi-deterministic Büchi automata into deterministic Muller automata.
Intro Slides 6, Lecture Notes 6
- Lecture 7, Nov 27, 2012
After completing the proof of McNaughton’s Theorem, we started our discussion of logics over infinite sequences. We introduced linear-time temporal logic (LTL), Quantified Propositional Temporal Logic (QPTL), and the second-order theory of 1 successor (S1S) and proved that the models of an LTL formula form a non-counting language.
Intro Slides 7, Lecture Notes 7 (updated on Feb 12, 2013)
- Lecture 8, Dec 4, 2012
We proved that QPTL, S1S, WS1S, and Büchi automata are equally expressive (while LTL is strictly weaker). Next, we defined alternating Büchi automata.
Intro Slides 8, Lecture Notes 8
- Lecture 9, Dec 11, 2012
We translated LTL formulas to alternating automata and proved that alternating Büchi automata recognize the same languages as nondeterministic Büchi automata (Miyano and Hayashi, 1984).
Intro Slides 9, Lecture Notes 9 (updated on Jan 7, 2013)
- Lecture 10, December 18, 2012
We proved memoryless determinacy for reachability and Büchi games.
Intro Slides 10, Lecture Notes 10 (updated on Jan 9, 2013)
- Lecture 12, January 15, 2013
We got started with the proof that parity tree automata are closed under complement.
Lecture Notes 12
- Lecture 13, January 22, 2013
We completed the proof that parity tree automata are closed under complement and introduced S2S, the second-order theory of 2 successors.
Intro Slides 13, Lecture Notes 13
- Lecture 14, January 29, 2013
We introduced alternating tree automata and provided a translation from CTL formulas to alternating Büchi tree automata.
Intro Slides 14, Lecture Notes 14
- Lecture 15, February 5, 2013
We looked at various game-based temporal logics and wrapped up with a summary of the course’s main points.
Lecture Notes 15
