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DOI: 10.4230/LIPIcs.CONCUR.2025.9

A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games

Authors: Raphaël Berthon, Joost-Pieter Katoen, and Zihan Zhou

Published in: LIPIcs, Volume 348, 36th International Conference on Concurrency Theory (CONCUR 2025)

Abstract

Significant progress has been recently achieved in developing efficient solutions for simple stochastic games (SSGs), focusing on reachability objectives. While reductions from stochastic parity games (SPGs) to SSGs have been presented in the literature through the use of multiple intermediate game models, a direct and simple reduction has been notably absent. This paper introduces a novel and direct polynomial-time reduction from quantitative SPGs to quantitative SSGs. By leveraging a gadget-based transformation that effectively removes the priority function, we construct an SSG that simulates the behavior of a given SPG. We formally establish the correctness of our direct reduction. Furthermore, we demonstrate that under binary encoding this reduction is polynomial, thereby directly corroborating the known NP ∩ coNP complexity of SPGs and providing new understanding in the relationship between parity and reachability objectives in turn-based stochastic games.

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Raphaël Berthon, Joost-Pieter Katoen, and Zihan Zhou. A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games. In 36th International Conference on Concurrency Theory (CONCUR 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 348, pp. 9:1-9:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{berthon_et_al:LIPIcs.CONCUR.2025.9,
  author =	{Berthon, Rapha\"{e}l and Katoen, Joost-Pieter and Zhou, Zihan},
  title =	{{A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games}},
  booktitle =	{36th International Conference on Concurrency Theory (CONCUR 2025)},
  pages =	{9:1--9:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-389-8},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{348},
  editor =	{Bouyer, Patricia and van de Pol, Jaco},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2025.9},
  URN =		{urn:nbn:de:0030-drops-239595},
  doi =		{10.4230/LIPIcs.CONCUR.2025.9},
  annote =	{Keywords: stochastic games, parity, reduction}
}

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DOI: 10.4230/LIPIcs.ICALP.2017.121

Threshold Constraints with Guarantees for Parity Objectives in Markov Decision Processes

Authors: Raphaël Berthon, Mickael Randour, and Jean-François Raskin

Published in: LIPIcs, Volume 80, 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)

Abstract

The beyond worst-case synthesis problem was introduced recently by Bruyère et al. [BFRR14]: it aims at building system controllers that provide strict worst-case performance guarantees against an antagonistic environment while ensuring higher expected performance against a stochastic model of the environment. Our work extends the framework of [Bruyère/Filiot/Randour/Raskin, STACS 2014] and follow-up papers, which focused on quantitative objectives, by addressing the case of omega-regular conditions encoded as parity objectives, a natural way to represent functional requirements of systems. We build strategies that satisfy a main parity objective on all plays, while ensuring a secondary one with sufficient probability. This setting raises new challenges in comparison to quantitative objectives, as one cannot easily mix different strategies without endangering the functional properties of the system. We establish that, for all variants of this problem, deciding the existence of a strategy lies in NP and in coNP, the same complexity class as classical parity games. Hence, our framework provides additional modeling power while staying in the same complexity class.

Cite as

Raphaël Berthon, Mickael Randour, and Jean-François Raskin. Threshold Constraints with Guarantees for Parity Objectives in Markov Decision Processes. In 44th International Colloquium on Automata, Languages, and Programming (ICALP 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 80, pp. 121:1-121:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{berthon_et_al:LIPIcs.ICALP.2017.121,
  author =	{Berthon, Rapha\"{e}l and Randour, Mickael and Raskin, Jean-Fran\c{c}ois},
  title =	{{Threshold Constraints with Guarantees for Parity Objectives in Markov Decision Processes}},
  booktitle =	{44th International Colloquium on Automata, Languages, and Programming (ICALP 2017)},
  pages =	{121:1--121:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-041-5},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{80},
  editor =	{Chatzigiannakis, Ioannis and Indyk, Piotr and Kuhn, Fabian and Muscholl, Anca},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2017.121},
  URN =		{urn:nbn:de:0030-drops-74360},
  doi =		{10.4230/LIPIcs.ICALP.2017.121},
  annote =	{Keywords: Markov decision processes, parity objectives, beyond worst-case synthesis}
}

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Documents authored by Berthon, Raphaël

A Direct Reduction from Stochastic Parity Games to Simple Stochastic Games

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Threshold Constraints with Guarantees for Parity Objectives in Markov Decision Processes

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