Infinite-state energy games

P. Abdulla, M. Atig, Piotr Hofman, Richard Mayr, K. N. Kumar, Patrick Totzke
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引用次数: 19

Abstract

Energy games are a well-studied class of 2-player turn-based games on a finite graph where transitions are labeled with integer vectors which represent changes in a multidimensional resource (the energy). One player tries to keep the cumulative changes non-negative in every component while the other tries to frustrate this. We consider generalized energy games played on infinite game graphs induced by pushdown automata (modelling recursion) or their subclass of one-counter automata. Our main result is that energy games are decidable in the case where the game graph is induced by a one-counter automaton and the energy is one-dimensional. On the other hand, every further generalization is undecidable: Energy games on one-counter automata with a 2-dimensional energy are undecidable, and energy games on pushdown automata are undecidable even if the energy is one-dimensional. Furthermore, we show that energy games and simulation games are inter-reducible, and thus we additionally obtain several new (un)decidability results for the problem of checking simulation preorder between pushdown automata and vector addition systems.
无限状态能量博弈
能量游戏是一种基于有限图形的2人回合制游戏,其中转换被标记为整数向量,表示多维资源(能量)的变化。一名玩家试图在每个组件中保持累积变化的非负性,而另一名玩家则试图挫败这一点。研究了由下推自动机(建模递归)或其子类一元自动机诱导的无限博弈图上的广义能量博弈。我们的主要结果是,当游戏图由单计数器自动机诱导且能量是一维的情况下,能量游戏是可决定的。另一方面,每一个进一步的推广都是不确定的:具有二维能量的单计数器自动机上的能量博弈是不确定的,即使能量是一维的,下推自动机上的能量博弈也是不确定的。此外,我们还证明了能量博弈和模拟博弈是可约的,从而得到了下推自动机和向量加法系统之间的模拟预序检验问题的几个新的(非)可判定性结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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