License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.MFCS.2016.8
URN: urn:nbn:de:0030-drops-64985
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Akshay, S. ; Bouyer, Patricia ; Krishna, Shankara Narayanan ; Manasa, Lakshmi ; Trivedi, Ashutosh

Stochastic Timed Games Revisited

LIPIcs-MFCS-2016-8.pdf (0.6 MB)


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.

BibTeX - Entry

  author =	{S. Akshay and Patricia Bouyer and Shankara Narayanan Krishna and Lakshmi Manasa and Ashutosh Trivedi},
  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 =	{Piotr Faliszewski and Anca Muscholl and Rolf Niedermeier},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{},
  URN =		{urn:nbn:de:0030-drops-64985},
  doi =		{10.4230/LIPIcs.MFCS.2016.8},
  annote =	{Keywords: timed automata, stochastic games, two-counter machines}

Keywords: timed automata, stochastic games, two-counter machines
Collection: 41st International Symposium on Mathematical Foundations of Computer Science (MFCS 2016)
Issue Date: 2016
Date of publication: 19.08.2016

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