Reachability switching games

John Fearnley; Martin Gairing; Matthias Mnich; Rahul Savani

doi:10.4230/LIPIcs.ICALP.2018.124

Reachability switching games

John Fearnley, Martin Gairing, Matthias Mnich, Rahul Savani

QE Operations research

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

Abstract

In this paper, we study the problem of deciding the winner of reachability switching games. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP n coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. We also study the structure of winning strategies in these games, and in particular we show that exponential memory is required in both the one- and two-player settings.

Original language	English
Title of host publication	45th International Colloquium on Automata, Languages, and Programming, ICALP 2018
Editors	Christos Kaklamanis, Daniel Marx, Ioannis Chatzigiannakis, Donald Sannella
Publisher	Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
Pages	124:1-124:14
Volume	107
ISBN (Electronic)	9783959770767
DOIs	https://doi.org/10.4230/LIPIcs.ICALP.2018.124
Publication status	Published - 1 Jul 2018
Event	45th International Colloquium on Automata, Languages, and Programming - Prague, Czech Republic Duration: 9 Jul 2018 → 13 Jul 2018 Conference number: 45

Publication series

Series	Leibniz International Proceedings in Informatics, LIPIcs
Number	124
Volume	107
ISSN	1868-8969

Conference

Conference	45th International Colloquium on Automata, Languages, and Programming
Abbreviated title	ICALP 2018
Country/Territory	Czech Republic
City	Prague
Period	9/07/18 → 13/07/18

Keywords

Deterministic random walks
Model checking
Reachability
Simple stochastic game
Switching systems

Access to Document

10.4230/LIPIcs.ICALP.2018.124Licence: CC BY

Cite this

Fearnley, J., Gairing, M., Mnich, M., & Savani, R. (2018). Reachability switching games. In C. Kaklamanis, D. Marx, I. Chatzigiannakis, & D. Sannella (Eds.), 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 (Vol. 107, pp. 124:1-124:14). Article 124 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. https://doi.org/10.4230/LIPIcs.ICALP.2018.124

Fearnley, John ; Gairing, Martin ; Mnich, Matthias et al. / Reachability switching games. 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. editor / Christos Kaklamanis ; Daniel Marx ; Ioannis Chatzigiannakis ; Donald Sannella. Vol. 107 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. pp. 124:1-124:14 (Leibniz International Proceedings in Informatics, LIPIcs; No. 124, Vol. 107).

@inproceedings{7626980176244439b4673ba48a360b1b,

title = "Reachability switching games",

abstract = "In this paper, we study the problem of deciding the winner of reachability switching games. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP n coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. We also study the structure of winning strategies in these games, and in particular we show that exponential memory is required in both the one- and two-player settings.",

keywords = "Deterministic random walks, Model checking, Reachability, Simple stochastic game, Switching systems",

author = "John Fearnley and Martin Gairing and Matthias Mnich and Rahul Savani",

note = "Funding Information: Supported by ERC Starting Grant 306465 (BeyondWorstCase) and DFG grant MN 59/4-1. Funding Information: 1 Supported by ERC Starting Grant 306465 (BeyondWorstCase) and DFG grant MN 59/4-1. Publisher Copyright: {\textcopyright} 2018 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.; 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018 ; Conference date: 09-07-2018 Through 13-07-2018",

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doi = "10.4230/LIPIcs.ICALP.2018.124",

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pages = "124:1--124:14",

editor = "Christos Kaklamanis and Daniel Marx and Ioannis Chatzigiannakis and Donald Sannella",

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Fearnley, J, Gairing, M, Mnich, M & Savani, R 2018, Reachability switching games. in C Kaklamanis, D Marx, I Chatzigiannakis & D Sannella (eds), 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. vol. 107, 124, Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, Leibniz International Proceedings in Informatics, LIPIcs, no. 124, vol. 107, pp. 124:1-124:14, 45th International Colloquium on Automata, Languages, and Programming, Prague, Czech Republic, 9/07/18. https://doi.org/10.4230/LIPIcs.ICALP.2018.124

Reachability switching games. / Fearnley, John; Gairing, Martin; Mnich, Matthias et al.
45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. ed. / Christos Kaklamanis; Daniel Marx; Ioannis Chatzigiannakis; Donald Sannella. Vol. 107 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing, 2018. p. 124:1-124:14 124 (Leibniz International Proceedings in Informatics, LIPIcs; No. 124, Vol. 107).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceeding › Academic › peer-review

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N2 - In this paper, we study the problem of deciding the winner of reachability switching games. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP n coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. We also study the structure of winning strategies in these games, and in particular we show that exponential memory is required in both the one- and two-player settings.

AB - In this paper, we study the problem of deciding the winner of reachability switching games. We study zero-, one-, and two-player variants of these games. We show that the zero-player case is NL-hard, the one-player case is NP-complete, and that the two-player case is PSPACE-hard and in EXPTIME. For the zero-player case, we also show P-hardness for a succinctly-represented model that maintains the upper bound of NP n coNP. For the one- and two-player cases, our results hold in both the natural, explicit model and succinctly-represented model. We also study the structure of winning strategies in these games, and in particular we show that exponential memory is required in both the one- and two-player settings.

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KW - Simple stochastic game

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BT - 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018

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A2 - Chatzigiannakis, Ioannis

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Fearnley J, Gairing M, Mnich M, Savani R. Reachability switching games. In Kaklamanis C, Marx D, Chatzigiannakis I, Sannella D, editors, 45th International Colloquium on Automata, Languages, and Programming, ICALP 2018. Vol. 107. Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. 2018. p. 124:1-124:14. 124. (Leibniz International Proceedings in Informatics, LIPIcs; No. 124, Vol. 107). doi: 10.4230/LIPIcs.ICALP.2018.124