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Documents authored by Prakash, Aditya

Document
DOI: 10.4230/LIPIcs.CSL.2025.22
On the Minimisation of Deterministic and History-Deterministic Generalised (Co)Büchi Automata

Authors: Antonio Casares, Olivier Idir, Denis Kuperberg, Corto Mascle, and Aditya Prakash

Published in: LIPIcs, Volume 326, 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)

Abstract
We present a polynomial-time algorithm minimising the number of states of history-deterministic generalised coBüchi automata, building on the work of Abu Radi and Kupferman on coBüchi automata. On the other hand, we establish that the minimisation problem for both deterministic and history-deterministic generalised Büchi automata is NP-complete, as well as the problem of minimising at the same time the number of states and colours of history-deterministic generalised coBüchi automata.
Cite as

Antonio Casares, Olivier Idir, Denis Kuperberg, Corto Mascle, and Aditya Prakash. On the Minimisation of Deterministic and History-Deterministic Generalised (Co)Büchi Automata. In 33rd EACSL Annual Conference on Computer Science Logic (CSL 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 326, pp. 22:1-22:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{casares_et_al:LIPIcs.CSL.2025.22,
  author =	{Casares, Antonio and Idir, Olivier and Kuperberg, Denis and Mascle, Corto and Prakash, Aditya},
  title =	{{On the Minimisation of Deterministic and History-Deterministic Generalised (Co)B\"{u}chi Automata}},
  booktitle =	{33rd EACSL Annual Conference on Computer Science Logic (CSL 2025)},
  pages =	{22:1--22:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-362-1},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{326},
  editor =	{Endrullis, J\"{o}rg and Schmitz, Sylvain},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2025.22},
  URN =		{urn:nbn:de:0030-drops-227798},
  doi =		{10.4230/LIPIcs.CSL.2025.22},
  annote =	{Keywords: Automata minimisation, omega-regular languages, good-for-games automata}
}
Document
DOI: 10.4230/LIPIcs.CONCUR.2024.12
History-Determinism vs Fair Simulation

Authors: Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract
An automaton 𝒜 is history-deterministic if its nondeterminism can be resolved on the fly, only using the prefix of the word read so far. This mild form of nondeterminism has attracted particular attention for its applications in synthesis problems. An automaton 𝒜 is guidable with respect to a class C of automata if it can fairly simulate every automaton in C, whose language is contained in that of 𝒜. In other words, guidable automata are those for which inclusion and simulation coincide, making them particularly interesting for model-checking. We study the connection between these two notions, and specifically the question of when they coincide. For classes of automata on which they do, deciding guidability, an otherwise challenging decision problem, reduces to deciding history-determinism, a problem that is starting to be well-understood for many classes. We provide a selection of sufficient criteria for a class of automata to guarantee the coincidence of the notions, and use them to show that the notions coincide for the most common automata classes, among which are ω-regular automata and many infinite-state automata with safety and reachability acceptance conditions, including vector addition systems with states, one-counter nets, pushdown-, Parikh-, and timed-automata. We also demonstrate that history-determinism and guidability do not always coincide, for example, for the classes of timed automata with a fixed number of clocks.
Cite as

Udi Boker, Thomas A. Henzinger, Karoliina Lehtinen, and Aditya Prakash. History-Determinism vs Fair Simulation. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 12:1-12:16, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{boker_et_al:LIPIcs.CONCUR.2024.12,
  author =	{Boker, Udi and Henzinger, Thomas A. and Lehtinen, Karoliina and Prakash, Aditya},
  title =	{{History-Determinism vs Fair Simulation}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{12:1--12:16},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.12},
  URN =		{urn:nbn:de:0030-drops-207841},
  doi =		{10.4230/LIPIcs.CONCUR.2024.12},
  annote =	{Keywords: History-Determinism}
}
Document
Track B: Automata, Logic, Semantics, and Theory of Programming
DOI: 10.4230/LIPIcs.ICALP.2024.124
Lookahead Games and Efficient Determinisation of History-Deterministic Büchi Automata

Authors: Rohan Acharya, Marcin Jurdziński, and Aditya Prakash

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

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.
Cite as

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)

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@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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