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In this paper, we look at good-for-games Rabin automata that recognise aMuller language (a language that is entirely characterised by the set ofletters that appear infinitely often in each word). We establish that minimalsuch automata are exactly of the same size as the minimal memory required forwinning Muller games that have this language as their winning condition. Weshow how to effectively construct such minimal automata. Finally, we establishthat these automata can be exponentially more succinct than equivalentdeterministic ones, thus proving as a consequence that chromatic memory forwinning a Muller game can be exponentially larger than unconstrained memory.

On the size of good-for-games Rabin automata and its link with the memory in Muller games