Prefix-independent objectives over finite colors are positionally determined on vertex-colored one- and two-player games iff they are generalized parity objectives on ordered pairs of colors.
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2 Pith papers cite this work, alongside 1 external citations. Polarity classification is still indexing.
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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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Positional Determinacy with Colored Vertices: a 1-to-2-Player Lift
Prefix-independent objectives over finite colors are positionally determined on vertex-colored one- and two-player games iff they are generalized parity objectives on ordered pairs of colors.
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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.