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TACL 2015 Summer School: Automata, Logic and Games: Theory and Application
# Automata, Logic and Games: Theory and Application

## Course Abstract

In Part 1 of the course, we introduce the mathematical theory
underpinning the model checking of computing systems. The main
ingredients are:

- Automata on infinite trees as a computational model of state-based systems.
- Logical systems, such as the modal mu-calculus and monadic
second-order logic, for describing correctness properties.
- Two-person games as a conceptual basis for understanding the
interactions between a system and its environment.

Some topics: decidability of the MSO theory of the full binary tree,
and its consequences; connections between parity games, modal
mu-calculus, and alternating parity tree automata, and the sense in
which they are equivalent.

Building on these foundations, we discuss, in Part 2, recent
developments in high-order model checking, the model checking of
infinite trees generated by higher-order recursion schemes (or
equivalently lambda-Y calculus). Some topics: decidability of
higher-order model checking with respect to modal mu-calculus, and
compositional model checking of higher-type Böhm trees.

## Lecture Slides

- Büchi automata and S1S
- Parity games, tree automata and S2S
- Higher-order model checking 1
- Higher-order model checking 2

## References

- Luke Ong: Automata, Logic and Games, Lecture Notes, University of Oxford, 2015.
- Luke Ong: Higher-Order Model Checking: An Overview, LICS 2015.