Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 104-04. Randomized quasipolynomial-time mean-payoff games
Manuscript map · lines 4535–4544
OpenAI@2026-10-07#rem:oai-p-104-04
Authors: OpenAI. Family 104.
Title: Randomized quasipolynomial-time mean-payoff games.
Abstract: We give a randomized algorithm that computes the complete zero-threshold winning set of a finite mean-payoff game with arbitrary signed integer edge weights encoded in binary. For total explicit input length L, it uses $2{}{O(({}log(L+2)){}2)}$ bit operations on every random tape and is correct with probability at least 7/8. A polynomial-time check certifies the winning regions and positional strategies for both players or reports failure. Independent repetition therefore gives an always-correct algorithm with the same expected quasipolynomial bit bound.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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