Deterministic quasipolynomial-time mean-payoff games

OpenAI

For an ordinary mean-payoff game of complete binary input length L with arbitrary signed binary edge weights, the September 25 deterministic manuscript reports a 2^O((log(L+2))²)-bit-operation algorithm for the exact winning set, values and optimal positional strategies.

Sources for this record

What was already known

Known general algorithms had pseudo-polynomial dependence on weight magnitude, which can be exponential in binary input length.

AI involvement AI-led

OpenAI attributes the result-104 mathematical manuscripts to an internal model. The release does not document an independent human origin for the central algorithm or enough detail for an autonomy rating.

The release credits an internal model with the mathematical result, without evidence of unsteered autonomy.

Importance Major

The deterministic bound removes that weight-size barrier for ordinary mean-payoff games.

Limitations

No completed check of this deterministic algorithm is documented. The available Lean theorem checks a different randomized zero-threshold algorithm; later stochastic and parity-game extensions are separate claims.

Technical verification Reported

No completed check of the deterministic algorithm is documented; the Lean theorem covers a different randomized claim.

Human understanding Few

No named person explains the deterministic algorithm’s central mechanism; Few is the evidence default.

Correction and publication history

2026-10-18 · publication

The ordinary deterministic binary-weight values-and-strategies result is separate from the existing stochastic mean-payoff publication and the randomized Lean theorem.

Read this published revision