Lecture Notes
- Lecture 1, Apr 17, 2008
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 24, 2008
We studied the expressiveness of deterministic and nondeterministic Büchi automata 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, May 8, 2008
We started 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
Summary Slides 3
- Lecture 5, May 29, 2008
We started the proof of McNaughton’s Theorem (1966): Every Büchi-recognizable language is recognizable by a deterministic Muller automaton.
Lecture Notes 5
Summary Slides 5
- Lecture 6, June 5, 2008
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, June 12, 2008
We introduced Quantified Propositional Temporal Logic (QPTL), which is LTL extended by quantification over propositional variables, and the Second-order theory of 1 Successor (S1S). QPTL, S1S, and Büchi automata are equally expressive, while LTL is strictly weaker.
Lecture Notes 7
Summary Slides 7
- Lecture 8, June 19, 2008
We completed our tour through the various logics over infinite sequences by proving that S1S and its weak version WS1S are equally expressive. After a quick look at two verification tools (SPIN and MONA), we introduced alternation and developed a translation from LTL formulas to alternating Büchi automata.
Lecture Notes 8
Summary Slides 8
- Lecture 9, June 26, 2008
We proved that alternating Büchi automata can be translated into equivalent nondeterministic Büchi automata (Miyano and Hayashi, 1984).
Lecture Notes 9
Summary Slides 9
- Lecture 12, July 17, 2008
We proved that parity tree automata are closed under complement, took a quick look at applications of tree automata in logics (S2S), and wrapped up with a review of the course’s main points.
Lecture Notes 12
Course Summary Slides
