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Lecture 11 Polynomial Time Hierarchy

This lecture explores the concept of polynomial-time Turing-reducibility and its implications in the polynomial-time hierarchy. It defines the relationship between languages A and B in terms of Turing machines with oracle access and presents key examples. The discussion includes formal definitions, theorems, and proofs, particularly focusing on PSPACE and its characterization through induction. The lecture aims to clarify the significance of polynomial time in computational complexity and the role of oracle machines in understanding these relationships.

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Lecture 11 Polynomial Time Hierarchy

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  1. Lecture 11Polynomial Time Hierarchy

  2. Oracle TM Query tape yes Query state no Remark:

  3. A is polynomial-time Turing-reducible to B if there exists a polynomial-time DTM with oracle B, accepting A.

  4. Example

  5. Example

  6. Definition

  7. Definition

  8. Definition Remark

  9. Theorem Proof

  10. PSPACE P

  11. Characterization THEOREM PROOF by induction on k

  12. Induction Step on k>1

  13. Characterization THEOREM PROOF by induction on k

  14. Induction Step on k>1

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