Sure-almost-sure and sure-limit-sure window mean-payoff problems in MDPs are in P (fixed, unary window) and NP∩coNP (bounded), matching separate sure and almost-sure complexities.
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Prefix-independent Σ₀² objectives with neutral letters are positional over arbitrary graphs exactly when recognized by history-deterministic monotone co-Büchi automata over countable ordinals, with proofs for mean-payoff positionality and a completeness lifting from finite graphs.
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Sure-almost-sure and Sure-limit-sure Window Mean Payoff in Markov Decision Processes
Sure-almost-sure and sure-limit-sure window mean-payoff problems in MDPs are in P (fixed, unary window) and NP∩coNP (bounded), matching separate sure and almost-sure complexities.
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Positionality in $\Sigma_0^2$ and a completeness result
Prefix-independent Σ₀² objectives with neutral letters are positional over arbitrary graphs exactly when recognized by history-deterministic monotone co-Büchi automata over countable ordinals, with proofs for mean-payoff positionality and a completeness lifting from finite graphs.