Alphabeta MathHow statement and proof provenance work
The first chip identifies the source of the statement or construction; the second identifies the source of its local proof or verification.
- Literature-sourced: the exact statement appears in a cited source; only wording and notation differ.
- AI-adapted: a semantically identical restatement of literature-sourced material, modulo indexing, notation, and boundary cases adopted by the library.
- AI-generated: a genuinely novel statement formulated by AI, with no source for the claim itself.
These labels describe origin, not correctness: citations and verification chips remain separate evidence.
FALSE: reusing the same random bits amplifies success
Statement
Reusing the same random bits amplifies success.
Facts & Assumptions
Given: the usual repetition-based amplification scheme.
Exponentially small BPP error is obtained by running independent trials and taking the majority answer (BPP amplification to exponentially small error).
Refutation
The hypothesis of [L1] is independence of the repeated trials. If the same random string is reused, the repeated executions become perfectly correlated instead of independent.
A perfectly correlated sequence of repetitions gives the same answer every time, so a majority vote over those repetitions agrees with one run and cannot improve its success probability. Therefore the statement is false.
Depends on
Used by
Dependency tree · two levels
3 results within two dependency steps of this one, each drawn at its shortest distance from it. An arrow runs from a result to what uses it, so the chart reads left to right and ends at this result, which carries a heavier outline. Every node is a link to that result. Click elsewhere on the chart to enlarge it.
Sources
- Sanjeev Arora and Boaz Barak, Computational Complexity: A Modern Approach (standard reference, not scraped)
- Eric Blais, Models of Computation, 14. Randomized Computation (standard reference, not scraped)