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

Antonio Casares, Thomas Colcombet, Karoliina Lehtinen
2022 arXiv   pre-print
In this paper, we look at good-for-games Rabin automata that recognise a Muller language (a language that is entirely characterised by the set of letters that appear infinitely often in each word). We establish that minimal such automata are exactly of the same size as the minimal memory required for winning Muller games that have this language as their winning condition. We show how to effectively construct such minimal automata. Finally, we establish that these automata can be exponentially
more » ... re succinct than equivalent deterministic ones, thus proving as a consequence that chromatic memory for winning a Muller game can be exponentially larger than unconstrained memory.
arXiv:2204.11333v2 fatcat:wqcrwl6d5naf5o6moyciuqexfi