We study the expressiveness and succinctness of good-for-games pushdown automata (GFG-PDA) over finite words, that is, pushdown automata whose nondeterminism can be resolved based on the run constructed so far, but independently of the remainder of the input word. We prove that GFG-PDA recognise more languages than deterministic PDA (DPDA) but not all context-free languages (CFL). This class is orthogonal to unambiguous CFL. We further show that GFG-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than GFG-PDA. We also study GFGness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show GFGness to be EXPTIME-complete. GFG-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than GFG-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in GFG-PDA. Every GFG-PDA has a positional resolver, a function that resolves nondeterminism and that is only dependant on the current configuration. Pushdown transducers are sufficient to implement the resolvers of GFG-VPA, but not those of GFG-PDA. GFG-PDA with finite-state resolvers are determinisable.

中文翻译：

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一点不确定性使下推自动机富有表现力和简洁性

我们研究了有限条件单词上的好游戏下推自动机（GFG-PDA）的表达性和简洁性，即下推自动机的不确定性可以根据到目前为止构建的运行来解决，但与输入单词的其余部分无关。我们证明GFG-PDA比确定性PDA（DPDA）识别更多的语言，但不是所有上下文无关的语言（CFL）。此类与明确的CFL正交。我们进一步表明，GFG-PDA可以比DPDA更加简洁，而PDA可以比GFG-PDA更加简洁。我们还研究了可视下推自动机（VPA）中的GFGness，该方法比PDA具有更好的闭合特性，并且我们证明GFGness是EXPTIME完全的。GFG-VPA可以比确定性VPA指数式简洁，而VPA可以比GFG-VPA指数式简洁。这两个下限都很严格。最后，我们研究了在GFG-PDA中解决不确定性的复杂性。每个GFG-PDA都有一个位置解析器，该功能可以解析不确定性，并且仅取决于当前配置。下推式传感器足以实现GFG-VPA的旋转变压器，但不足以实现GFG-PDA的旋转变压器。具有有限状态解析器的GFG-PDA是可确定的。