HOA non-emptiness is NP-complete for standard acceptance conditions; inclusion is PSPACE-complete except EXPSPACE-complete for Emerson-Lei; HOG games are Pi2-complete for parity/safety and PSPACE-complete for Muller/Emerson-Lei.
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A Theory of Hanoi Omega-Automata and Games
HOA non-emptiness is NP-complete for standard acceptance conditions; inclusion is PSPACE-complete except EXPSPACE-complete for Emerson-Lei; HOG games are Pi2-complete for parity/safety and PSPACE-complete for Muller/Emerson-Lei.