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Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata

Authors Rohan Acharya, Marcin Jurdziński , Aditya Prakash

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ACM Subject Classification
  • Theory of computation → Automata over infinite objects
Keywords
  • History determinism
  • Good-for-games
  • Automata over infinite words
  • Games

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Abstract

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.

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Rohan Acharya, Marcin Jurdziński, and Aditya Prakash. Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 124:1-124:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024) https://doi.org/10.4230/LIPIcs.ICALP.2024.124

Author Details

Rohan Acharya
  • University of Warwick, Coventry, UK
Marcin Jurdziński
  • University of Warwick, Coventry, UK
Aditya Prakash
  • University of Warwick, Coventry, UK

Funding

We acknowledge the Centre for Discrete Mathematics and Its Applications (DIMAP) at the University of Warwick for partial support.
  • Acharya, Rohan: Undergraduate Research Support Scheme and the Department of Computer Science, University of Warwick.
  • Prakash, Aditya: Chancellors' International Scholarship from the University of Warwick.

Acknowledgements

We thank Udi Boker, Denis Kuperberg, and Karoliina Lehtinen for several insightful exchanges. We are grateful to the reviewers for their feedback and suggestions on how to improve the paper.

References

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