Games, Logic and Automata Seminar Rotem Zach 1

Overview 2

Notation 3

Recap 4

Büchi Acceptance [Büchi 1962] 5

Example Which language is recognized? 6

Deterministic Büchi Automata 7

Muller Acceptance [Muller 1963] 8

Example 9

10

11

12

13

Rabin Acceptance [Rabin 1969] 14

Example 15

Streett Acceptance [Streett 1982] 16

Example 17

18

19

Nondeterministic Equivalence 20

Parity Condition [Mostowski 1984] 21

Example 22

23

24

25

26

27

28

Closure Under Complement 29

D’ Muller -> D’ Streett 30

31

Deterministic Equivalence 32

Lower Bounds [Löding 1999] 33

Sources Grädel, Thomas, Wilke (Eds.): Automata, Logics, and Infinite Games: A Guide to Current Research, 2002 J.R. Büchi, On a decision method in restricted second order arithmetic, 1962 D.E. Muller, Infinite sequences and finite machines, 1963 M.O. Rabin, Decidability of second order theories and automata on infinite trees, 1969 R.S. Streett, Propositional dynamic logic of looping and converse is elementary decidable, 1982 A.W. Mostowski. Regular expressions for infnite trees and a standard form of automata, 1984 C. Löding, Optimal bounds for the transformation of omega-automata,

Questions? 35