## Klein, Felix and Zimmermann, Martin - How Much Lookahead is Needed to Win Infinite Games?

lmcs:2011 - Logical Methods in Computer Science, April 27, 2017, Volume 12, Issue 3 - https://doi.org/10.2168/LMCS-12(3:4)2016
How Much Lookahead is Needed to Win Infinite Games?

Authors: Klein, Felix and Zimmermann, Martin

Delay games are two-player games of infinite duration in which one player may delay her moves to obtain a lookahead on her opponent's moves. For $\omega$-regular winning conditions it is known that such games can be solved in doubly-exponential time and that doubly-exponential lookahead is sufficient. We improve upon both results by giving an exponential time algorithm and an exponential upper bound on the necessary lookahead. This is complemented by showing EXPTIME-hardness of the solution problem and tight exponential lower bounds on the lookahead. Both lower bounds already hold for safety conditions. Furthermore, solving delay games with reachability conditions is shown to be PSPACE-complete. This is a corrected version of the paper https://arxiv.org/abs/1412.3701v4 published originally on August 26, 2016.

Volume: Volume 12, Issue 3
Published on: April 27, 2017
Submitted on: October 29, 2015
Keywords: Computer Science - Computer Science and Game Theory,Computer Science - Formal Languages and Automata Theory