Abstract
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 Löding. 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.
The research leading to these results has received funding from the European Union’s Seventh Framework Programme (FP7/2007-2013) under grant agreement 259454 (GALE).
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Fijalkow, N., Horn, F., Kuperberg, D., Skrzypczak, M. (2015). Trading Bounds for Memory in Games with Counters. In: Halldórsson, M., Iwama, K., Kobayashi, N., Speckmann, B. (eds) Automata, Languages, and Programming. ICALP 2015. Lecture Notes in Computer Science(), vol 9135. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-47666-6_16
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DOI: https://doi.org/10.1007/978-3-662-47666-6_16
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