不安全高阶文法的Word语言和边缘语言
On Word and Frontier Languages of Unsafe Higher-Order Grammars
摘要：
高阶文法是常规文法和上下文无关文法的扩展，其中非终结符可以带参数。它们在80年代得到了广泛的研究，最近又在模型检验和程序验证的背景下得到了重新研究。我们证明了不安全序-（n+1）词语言类与不安全序-n树语言的边界语言类是一致的。我们使用交集类型来将一个n+1序词文法转换成一个相应的n序树文法。Damm在1982年已经证明了这个结果对于安全语言，但据我们所知，它对于不安全语言是开放的。各种已知的结果高阶文法可以得到几乎直接推论我们的结果。
英文摘要：
Higher-order grammars are extensions of regular and context-free grammars, where non-terminals may take parameters. They have been extensively studied in 1980's, and restudied recently in the context of model checking and program verification. We show that the class of unsafe order-(n+1) word languages coincides with the class of frontier languages of unsafe order-n tree languages. We use intersection types for transforming an order-(n+1) word grammar to a corresponding order-n tree grammar. The result has been proved for safe languages by Damm in 1982, but it has been open for unsafe languages, to our knowledge. Various known results on higher-order grammars can be obtained as almost immediate corollaries of our result.
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