2017/09/10 by Nathanaël Fijalkow, Florian Horn, Fijalkow, Nathanaël +5
Computer Science · #Computability, Logic, AI Algorithms #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic, programming, and type systems #semigroups and automata theory
paper · pdf · doi:10.48550/arxiv.1709.03121
openalex publication_date 2017/09/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 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.