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On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions [article]

Antonio Casares
2021 arXiv   pre-print
In this paper, we relate the problem of determining the chromatic memory requirements of Muller conditions with the minimisation of transition-based Rabin automata.  ...  Our first contribution is a proof of the NP-completeness of the minimisation of transition-based Rabin automata.  ...  We first remark that by Theorem 28, the size of a minimal arena-independent memory for F coincides with the size of a minimal Rabin automaton for L F .  ... 
arXiv:2105.12009v3 fatcat:53zbdhisnnathi2f74kdv4ke5u

On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory Requirements of Muller Conditions

Antonio Casares, Florin Manea, Alex Simpson
2022
In this paper, we relate the problem of determining the chromatic memory requirements of Muller conditions with the minimisation of transition-based Rabin automata.  ...  Our first contribution is a proof of the NP-completeness of the minimisation of transition-based Rabin automata.  ...  C S L 2 0 2 2 12:8 Minimisation of Rabin Automata and Chromatic Memory for Muller Conditions ▶ Remark 11.  ... 
doi:10.4230/lipics.csl.2022.12 fatcat:s5igjimcb5c5tpdx4bwuq34eke

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
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.  ...  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).  ...  Acknowledgements We would like to thank Marthe Bonamy and Pierre Charbit for their help with graph theory.  ... 
arXiv:2204.11333v2 fatcat:wqcrwl6d5naf5o6moyciuqexfi

Front Matter, Table of Contents, Preface, Conference Organization

Florin Manea, Alex Simpson
2022
Front Matter, Table of Contents, Preface, Conference Organization  ...  From these, the programme committee selected Antonio Casares as the recipient of the 2022 Helena Rasiowa Award, for his paper On the Minimisation of Transition-Based Rabin Automata and the Chromatic Memory  ...  Requirements of Muller Conditions.  ... 
doi:10.4230/lipics.csl.2022.0 fatcat:7zpob34yszbh5okf5pv2b5nsyq