文章基本信息

标题：Pumping Lemma for Higher-order Languages
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作者：Kazuyuki Asada ; Naoki Kobayashi
期刊名称：LIPIcs : Leibniz International Proceedings in Informatics
电子版ISSN：1868-8969
出版年度：2017
卷号：80
页码：97:1-97:14
DOI：10.4230/LIPIcs.ICALP.2017.97
出版社：Schloss Dagstuhl -- Leibniz-Zentrum fuer Informatik
摘要：We study a pumping lemma for the word/tree languages generated by higher-order grammars. Pumping lemmas are known up to order-2 word languages (i.e., for regular/context-free/indexed languages), and have been used to show that a given language does not belong to the classes of regular/context-free/indexed languages. We prove a pumping lemma for word/tree languages of arbitrary orders, modulo a conjecture that a higher-order version of Kruskal's tree theorem holds. We also show that the conjecture indeed holds for the order-2 case, which yields a pumping lemma for order-2 tree languages and order-3 word languages.
关键词：pumping lemma; higher-order grammars; Kruskal's tree theorem