How Much Lookahead is Needed to Win Infinite Games?

Felix Klein and Martin Zimmermann

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 by 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.

Logical Methods in Computer Science (LMCS).

(pdf) (bib)