Write down precise constants in the asymptotic complexity #3
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girving
commented
Aug 16, 2024
girving
commented
- Alice takes 5000 k^2 t log t + smaller terms
- Bob takes 20000/9 k^2 t log t + smaller terms
- Vera takes 106000 * k^2 + 1
1. Alice takes 5000 k^2 t log t + smaller terms 2. Bob takes 20000/9 k^2 t log t + smaller terms 3. Vera takes 106000 * k^2 + 1
Thanks to Ruben Van de Velde for pointing this out! https://leanprover.zulipchat.com/#narrow/stream/217875-Is-there-code-for-X.3F/topic/log.20200.20*.2020000.20.E2.89.A4.20106000/near/444895276
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@eric-wieser Next one: A bit of refactoring, and then writing down the constants. |
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(For more context: this is very much related to the original paper, and will be the last PR for a while based on recent discussions.) |
eric-wieser
reviewed
Aug 28, 2024
eric-wieser
approved these changes
Aug 28, 2024
| theorem bob_fast (k : ℝ) (k0 : 0 < k) (t : ℕ) (alice : Alice) (vera : Vera) : | ||
| let p := defaults k t k0 | ||
| (debate alice (bob p.s p.b p.q) vera t).cost' o BobId ≤ | ||
| (t+1) * (20000 / 9 * k^2 * Real.log (200 * (t+1)) + 1) := by |
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Is it feasible to write a version of this using asymptotics notation, that more closely resembles the docstring? (happy to merge without this)
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I want the explicit constant version: https://x.com/geoffreyirving/status/1805903946629701764
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Ah, you probably mean additionally have the asymptotic versions. I’d like to triage that away for now if possible.
eric-wieser
reviewed
Sep 9, 2024
Co-authored-by: Eric Wieser <wieser.eric@gmail.com>
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