~/talk

Information Complexity is Computable

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Proves zero‑error information complexity is algorithmically approximable: given f on n×m and distribution μ produce a δ‑approximation by restricting to protocols with explicitly bounded rounds w (roughly at most (n/ε)^{O(n)}), then enumerating protocol trees for f^k to estimate amortized cost. Key tools are discretizing message functions into a finite signal net, reducing signals to uniform weak ones and bundling into boxes to limit interaction, plus Markov tail bounds; runtime is enormous but finite (double/triple‑exponential).

AI-written summary · about

  1. 0:00Intro
  2. 0:27Information Complexity
  3. 3:39Computing IC
  4. 7:43Main Theorem
  5. 8:33Corollary
  6. 12:05The anatomy of a protocol
  7. 12:37Proof Overview
  8. 13:18Massaging the signals
  9. 14:10Reducing the number types of signals
  10. 19:36Selecting t
  11. 24:18Main Result
  12. 25:11Open problems
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