Trading Bounds for Memory in Games with Counters
We study two-player games with counters, where the objective of the first player is that the counter values remain bounded. We investigate the existence of a trade-off between the size of the memory and the bound achieved on the counters, which has been conjectured by Colcombet and Loeding.
We show that unfortunately this conjecture does not hold: there is no trade-off between bounds and memory, even for finite arenas. On the positive side, we prove the existence of a trade-off for the special case of thin tree arenas. This allows us to extend the theory of regular cost functions over thin trees, and obtain as a corollary the decidability of cost monadic second-order logic over thin trees.
This is joint work with Florian Horn, Denis Kuperberg, and Michal Skrzypczak.
Nathanael Fijalkow is a PhD student, jointly supervised by Thomas Colcombet (LIAFA, Paris 7, France) and Mikolaj Bojanczyk (University of Warsaw, Poland). His research interests include Automata, Games, Logics and Probabilistic Models of Computations.