3 research outputs found
Playing Muller Games in a Hurry
This work studies the following question: can plays in a Muller game be
stopped after a finite number of moves and a winner be declared. A criterion to
do this is sound if Player 0 wins an infinite-duration Muller game if and only
if she wins the finite-duration version. A sound criterion is presented that
stops a play after at most 3^n moves, where n is the size of the arena. This
improves the bound (n!+1)^n obtained by McNaughton and the bound n!+1 derived
from a reduction to parity games
Formats of Winning Strategies for Six Types of Pushdown Games
The solution of parity games over pushdown graphs (Walukiewicz '96) was the
first step towards an effective theory of infinite-state games. It was shown
that winning strategies for pushdown games can be implemented again as pushdown
automata. We continue this study and investigate the connection between game
presentations and winning strategies in altogether six cases of game arenas,
among them realtime pushdown systems, visibly pushdown systems, and counter
systems. In four cases we show by a uniform proof method that we obtain
strategies implementable by the same type of pushdown machine as given in the
game arena. We prove that for the two remaining cases this correspondence
fails. In the conclusion we address the question of an abstract criterion that
explains the results