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

@article{Casares2022OnTS, title={On the size of good-for-games Rabin automata and its link with the memory in Muller games}, author={Antonio Casares and Thomas Colcombet and Karoliina Lehtinen}, journal={ArXiv}, year={2022}, volume={abs/2204.11333} }

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…

## 2 Citations

Infinite Separation between General and Chromatic Memory

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In this note, we answer a question from [Alexander Kozachinskiy. State Complexity of Chromatic Memory in Inﬁnite-Duration Games, arXiv:2201.09297]. Namely, we construct a winning condition W over a…

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This paper characterize objectives recognizable by deterministic Büchi automata (a class of ω -regular objectives) that are half-positional, in both finite and infinite graphs, using the language-theoretic notion of right congruence.

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