1. Hierarchy Theorems

3. Space Hierarchy Theorem

12. Relativization

13. Limits of the Diagonalization Method

18. Circuit Complexity      x1x1 x2x2 x3x3 output

22. ⊔ 0⊔⊔0 1 q00q00 Cell[1,1] start configuration Cell[t(n),1] Accept position t(n)-th configuration

25. 001 0 0 10q 0 … 0q l 1q 0 … 1q l 0 1 …     …

30. Monotone Circuits

31. 12 3

33. Richard Rado 1906 --1989 Paul Erd ö s (3/26, 1913 – 9/20,1996 )

36. Plucking a sunflower      x 1 x 2 x 1 x 3 x 2 x 3   x 1 x 2 x 1 x 3 x 1 x 3 x 2 x 3  {x 1 x 2, x 1 x 3 }, { x 1 x 3, x 2 x 3 } {x 1 x 2 x 3, x 1 x 3 }

38. 

40. ........................ 1 2 3 K-1 …

41. Z

44. 