Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games
Claims a deterministic algorithm with bit operations that outputs the set of vertices of nonnegative value in finite turn-based stochastic mean-payoff games with signed binary rewards and arbitrary rational chance probabilities, and hence decides the threshold-1/2 problem for Condon's simple stochastic games in deterministic quasipolynomial time. The proof chooses an explicit discount of polynomial bit length and finds the discounted fixed point by a recursive labeling procedure. It does NOT give a polynomial-time algorithm, and it decides the threshold set rather than outputting values or strategies in the stated theorem.
Exact FrontierDelta
Scope and record
Occurred: Oct 5, 2026
Delta type: SOURCE CLAIM
Assumptions: VibeMathed verification: unreviewed. Publication: announcement. AI contribution: ai-discovered. VibeMathed editorial classifications, scores, notes, relations, and dataset structure are CC BY 4.0. Source statements and linked content retain their own rights.
Canonical aliases: Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games · Stochastic games in quasipolynomial time
Confidence: Not scored
Registry verification: unreviewed · announcement · partial
Attribution
VibeMathed
registry · event recorded by
Unreleased internal OpenAI model
model · ai model contributor · OpenAI
Lineage and corrections
VibeMathed record: Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games evidence for this event
This event attributed to Unreleased internal OpenAI model
Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games evidence for this event
Companion: Randomized quasipolynomial-time mean-payoff games evidence for this event
Companion: Deterministic quasipolynomial-time mean-payoff games evidence for this event
Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games parent of this event
Claims a deterministic algorithm with bit operations that outputs the set of vertices of nonnegative value in finite turn-based stochastic mean-payoff games with signed binary rewards and arbitrary rational chance probabilities, and hence decides the threshold-1/2 problem for Condon's simple stochastic games in deterministic quasipolynomial time. The proof chooses an explicit discount of polynomial bit length and finds the discounted fixed point by a recursive labeling procedure. It does NOT give a polynomial-time algorithm, and it decides the threshold set rather than outputting values or strategies in the stated theorem. parent of this event
Act on this frontier