We study the expressiveness and succinctness of history-deterministic pushdown automata (HD-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. These are also known as good-for-games automata. We prove that HD-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 HD-PDA can be exponentially more succinct than DPDA, while PDA can be double-exponentially more succinct than HD-PDA. We also study HDness in visibly pushdown automata (VPA), which enjoy better closure properties than PDA, and for which we show that deciding HDness is ExpTime-complete. HD-VPA can be exponentially more succinct than deterministic VPA, while VPA can be exponentially more succinct than HD-VPA. Both of these lower bounds are tight. Finally, we study the complexity of resolving nondeterminism in HD-PDA. Every HD-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 HD-VPA, but not those of HD-PDA. HD-PDA with finite-state resolvers are determinisable.
翻译:我们研究了历史-确定性自下自上而下自上而下(HD-PDA)对限定词的清晰度和简洁性,即,自上而下自下自上而上,其非确定性可以以迄今所建的运行为基础加以解决,但与输入词的其余部分无关。这些也被称为“为游戏好自上而上”。我们证明,HD-PDA承认的语言多于确定性自上而下PDA(DPDA),但并非所有不切实际的语言(CFL)。这一类与明确的CFL(C)相比是分级的。我们进一步表明,HD-DA(HD-DA)可以比DPDA(DPDA)更加简明,而PDA(PDA)可以比D-DA(HD-PA)更简明扼要,而PD(HD-DA)的快速自下而下而下而下而上,这种自下而上式的自下而下而下式的自下而下而上式的自下而下式的自下而下而下式的分辨率,这些自下而下式的自下而下而下而下而下而下而下而下。最后,这些自下即是,这些自下式的自下而下而下而下而下而下而下式的自下而下而下而下而下而下而下式的硬的分辨率的分辨率的分辨率的根的根的自上。