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Hierarchy Theorems

Hierarchy Theorems. Hierarchy Theorems. Space Hierarchy Theorem. Relativization. Limits of the Diagonalization Method. x 1. x 2. x 3. . . . . . . output. Circuit Complexity. start configuration. Cell[1,1]. ⊔. 0. 0⊔⊔. 1. q 0 0. Cell[t(n),1] Accept position. t(n)-th

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Hierarchy Theorems

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  1. Hierarchy Theorems

  2. Hierarchy Theorems

  3. Space Hierarchy Theorem

  4. Relativization

  5. Limits of the Diagonalization Method

  6. x1 x2 x3       output Circuit Complexity

  7. start configuration Cell[1,1] ⊔ 0 0⊔⊔ 1 q00 Cell[t(n),1] Accept position t(n)-th configuration

  8.    …

  9. Monotone Circuits

  10. 1 2 3

  11. Paul Erdös (3/26, 1913 – 9/20,1996) Richard Rado 1906 --1989

  12. Plucking a sunflower        {x1x2, x1x3}, {x1x3, x2x3} x1x2x1x3x1x3x2x3    {x1x2x3, x1x3} x1 x2 x1 x3 x2 x3

  14. . . . . . . . . . . . . . . . . . . . . . . . . 1 2 K-1 … 3

  15. Z

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