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We show that solving delay games with winning conditions given bydeterministic and nondeterministic weak Muller automata is 2EXPTIME-completerespectively 3EXPTIME-complete. Furthermore, doubly and triply exponentiallookahead is necessary and sufficient to win such games. These results are thefirst that show that the succinctness of the automata types used to specify thewinning conditions has an influence on the complexity of these problems.

Weak Muller Conditions Make Delay Games Hard