Our main technical contribution is a polynomial-time determinisation procedure for history-deterministic Büchi automata, which settles an open question of Kuperberg and Skrzypczak, 2015. A key conceptual contribution is the lookahead game, which is a variant of Bagnol and Kuperberg’s token game, in which Adam is given a fixed lookahead. We prove that the lookahead game is equivalent to the 1-token game. This allows us to show that the 1-token game characterises history-determinism for semantically-deterministic Büchi automata, which paves the way to our polynomial-time determinisation procedure.
@InProceedings{acharya_et_al:LIPIcs.ICALP.2024.124, author = {Acharya, Rohan and Jurdzi\'{n}ski, Marcin and Prakash, Aditya}, title = {{Lookahead Games and Efficient Determinisation of History-Deterministic B\"{u}chi Automata}}, booktitle = {51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)}, pages = {124:1--124:18}, series = {Leibniz International Proceedings in Informatics (LIPIcs)}, ISBN = {978-3-95977-322-5}, ISSN = {1868-8969}, year = {2024}, volume = {297}, editor = {Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola}, publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik}, address = {Dagstuhl, Germany}, URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.124}, URN = {urn:nbn:de:0030-drops-202672}, doi = {10.4230/LIPIcs.ICALP.2024.124}, annote = {Keywords: History determinism, Good-for-games, Automata over infinite words, Games} }
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