Quasipolynomial-time solution of simple stochastic and turn-based stochastic mean-payoff games

Claims a deterministic algorithm with $2^{O((\log(L+2))^2)}$ 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.

Claims a deterministic algorithm with $2^{O((\log(L+2))^2)}$ 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.