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DOI: 10.4230/LIPIcs.MFCS.2016.8

Stochastic Timed Games Revisited

Authors: S. Akshay, Patricia Bouyer, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi

Published in: LIPIcs, Volume 58, 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)

Abstract

Stochastic timed games (STGs), introduced by Bouyer and Forejt, naturally generalize both continuous-time Markov chains and timed automata by providing a partition of the locations between those controlled by two players (Player Box and Player Diamond) with competing objectives and those governed by stochastic laws. Depending on the number of players - 2, 1, or 0 - subclasses of stochastic timed games are often classified as 2 1/2-player, 1 1/2-player, and 1/2-player games where the 1/2 symbolizes the presence of the stochastic "nature" player. For STGs with reachability objectives it is known that 1 1/2-player one-clock STGs are decidable for qualitative objectives, and that 2 1/2-player three-clock STGs are undecidable for quantitative reachability objectives. This paper further refines the gap in this decidability spectrum. We show that quantitative reachability objectives are already undecidable for 1 1/2 player four-clock STGs, and even under the time-bounded restriction for 2 1/2-player five-clock STGs. We also obtain a class of 1 1/2, 2 1/2 player STGs for which the quantitative reachability problem is decidable.

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S. Akshay, Patricia Bouyer, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi. Stochastic Timed Games Revisited. In 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 58, pp. 8:1-8:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016)

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@InProceedings{akshay_et_al:LIPIcs.MFCS.2016.8,
  author =	{Akshay, S. and Bouyer, Patricia and Krishna, Shankara Narayanan and Manasa, Lakshmi and Trivedi, Ashutosh},
  title =	{{Stochastic Timed Games Revisited}},
  booktitle =	{41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)},
  pages =	{8:1--8:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-016-3},
  ISSN =	{1868-8969},
  year =	{2016},
  volume =	{58},
  editor =	{Faliszewski, Piotr and Muscholl, Anca and Niedermeier, Rolf},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2016.8},
  URN =		{urn:nbn:de:0030-drops-64985},
  doi =		{10.4230/LIPIcs.MFCS.2016.8},
  annote =	{Keywords: timed automata, stochastic games, two-counter machines}
}

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DOI: 10.4230/LIPIcs.FSTTCS.2015.261

Revisiting Robustness in Priced Timed Games

Authors: Shibashis Guha, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi

Published in: LIPIcs, Volume 45, 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)

Abstract

Priced timed games are optimal-cost reachability games played between two players---the controller and the environment---by moving a token along the edges of infinite graphs of configurations of priced timed automata. The goal of the controller is to reach a given set of target locations as cheaply as possible, while the goal of the environment is the opposite. Priced timed games are known to be undecidable for timed automata with 3 or more clocks, while they are known to be decidable for automata with 1 clock. In an attempt to recover decidability for priced timed games Bouyer, Markey, and Sankur studied robust priced timed games where the environment has the power to slightly perturb delays proposed by the controller. Unfortunately, however, they showed that the natural problem of deciding the existence of optimal limit-strategy---optimal strategy of the controller where the perturbations tend to vanish in the limit---is undecidable with 10 or more clocks. In this paper we revisit this problem and improve our understanding of the decidability of these games. We show that the limit-strategy problem is already undecidable for a subclass of robust priced timed games with 5 or more clocks. On a positive side, we show the decidability of the existence of almost optimal strategies for the same subclass of one-clock robust priced timed games by adapting a classical construction by Bouyer at al. for one-clock priced timed games.

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Shibashis Guha, Shankara Narayanan Krishna, Lakshmi Manasa, and Ashutosh Trivedi. Revisiting Robustness in Priced Timed Games. In 35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015). Leibniz International Proceedings in Informatics (LIPIcs), Volume 45, pp. 261-277, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2015)

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@InProceedings{guha_et_al:LIPIcs.FSTTCS.2015.261,
  author =	{Guha, Shibashis and Krishna, Shankara Narayanan and Manasa, Lakshmi and Trivedi, Ashutosh},
  title =	{{Revisiting Robustness in Priced Timed Games}},
  booktitle =	{35th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2015)},
  pages =	{261--277},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-97-2},
  ISSN =	{1868-8969},
  year =	{2015},
  volume =	{45},
  editor =	{Harsha, Prahladh and Ramalingam, G.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2015.261},
  URN =		{urn:nbn:de:0030-drops-56440},
  doi =		{10.4230/LIPIcs.FSTTCS.2015.261},
  annote =	{Keywords: Priced Timed Games, Decidability, Optimal strategies, Robustness}
}

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Stochastic Timed Games Revisited

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Revisiting Robustness in Priced Timed Games

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