发表机构
School of Informatics, Kochi University of Technology; Graduate School of Informatics, Nagoya University; School of Social Informatics, Mukogawa Women’s University（高知工科大学信息学部; 名古屋大学情报学府; 武库川女子大学社会信息学部）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文针对右线性文法上的成功推导游戏，构造了用于计算格伦迪数的DFA，证明对应格伦迪数集合为正则，推导得最小上界可判定，且该计算问题为PSPACE完全。
AI 中文摘要
Inoue等人提出了上下文无关文法（CFG）上的成功推导游戏（SDG），该游戏是经典基于堆游戏（包括减法游戏和凯尔斯游戏）的推广，他们还证明了对于给定CFG G上的SDG，即使将G限制为线性CFG，其格伦迪数的最小上界通常也是不可判定的。本文表明，对于右线性文法（RLG）上的SDG，我们可以构造一个DFA来计算给定位置的格伦迪数，换句话说，对于RLG上的SDG，具有给定格伦迪数c的位置集合是正则的。作为推论，给定RLG上SDG的格伦迪数的最小上界是可判定的。我们还研究了计算给定RLG上SDG的格伦迪数最小上界的复杂性，结果表明该问题是PSPACE完全的。
英文摘要
Inoue et al. have introduced the successful derivation game (SDG) on context-free grammars (CFGs), which is a generalization of classic heap-based games including subtraction games and Keyles, and shown that the least upper bound of the Grundy numbers in the SDG on a given CFG G is undecidable in general even when we restrict G to be a linear CFG. This paper shows that for the SDG on a right-linear grammar (RLG), we can construct a DFA for computing the Grundy number of a given position. In other words, for the SDG on an RLG, the set of positions with a given Grundy number c is regular. As a corollary, the least upper bound of the Grundy numbers in the SDG on a given RLG is decidable. We also investigate the complexity of computing the least upper bound of the Grundy numbers in the SDG on a given RLG, and it is shown to be PSPACE-complete.
