BPP Lifting and Its Applications

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" summary

Gives a constructive proof that randomized decision-tree complexity of any outer problem F lifts to randomized communication complexity of F composed with an index (pointer) gadget of size m = n^100 (asymmetric: Alice ~log m bits, Bob ~m bits). Builds a refined protocol that maintains density on X-blocks and largeness on Y, simulates messages by moving proportional to rectangle sizes, and shows transcript distributions differ by at most inverse-polynomial, yielding the BPP lifting theorem.

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" chapters (17)

1. 0:00Intro
2. 4:15Background
3. 4:33Lifting
4. 5:23Applications
5. 6:07Theorem
6. 9:04Randomized Decision Trees
7. 10:53Constructive Proof
8. 20:24Invariants
9. 22:27Simulation Overview
10. 23:07Decision Tree
11. 23:59Density Restoration
12. 28:12Refining the Protocol
13. 37:41The Whole Distribution
14. 39:20Uniform Marginals
15. 41:29Example A
16. 48:38Level K Inequality Lemma
17. 56:50Open Questions