1. LECTURE 2-9 PSPACE-Complete

2. SPACE BOUNDED HALTING PROBLEM (SBHP)
THEOREM
PROOF

3. QUANTIFIED BOOLEAN FORMULA
QBF
THEOREM

4. PROOF

8. 3-QBF
THEOREM

9. Geography Game

10. Example 1
BLUE ALWAYS WINS

11. Example 2
RED WINS

12. Example 2
BLUE WINS
IF RED DOESN’T MAKE A MISTAKE, THEN BLUE CANNOT WIN.

13. Example 3
BLUE HAS A WINNING STRATEGY!!!

14. Geography Problem
WIINNIG STRATEGY

15. THEOREM
PROOF
Construction
Such that

16. BLUE HAS A WINNING STRATEGY!!!

17. BLUE HAS A WINNING STRATEGY!!!

18. BLUE HAS A WINNING STRATEGY!!!
Means: there is an assignment for x-variables making every clause satisfied.

19. BLUE HAS A WINNING STRATEGY!!!

20. BLUE HAS A WINNING STRATEGY!!!

21. Questions Is go game on 19x19 grid PSPACE-complete?
What do we mean that the go game is PSPACE-complete?

22. Thanks, end.