Topic
Indexed language
About: Indexed language is a research topic. Over the lifetime, 334 publications have been published within this topic receiving 11000 citations.
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TL;DR: In this paper, a pumping lemma for the word/tree languages generated by higher-order grammars has been shown for order-2 tree languages and order-3 word languages.
Abstract: 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.
6 citations
Journal Article•
6 citations
01 Nov 1994
TL;DR: An infinite hierarchy of languages that comprises the context‐free languages as the first and all the languages generated by TAGs as the second element is obtained, which can be used for on‐line parsing of natural language.
Abstract: Coupled-context-free grammars are a natural generalisation of context-free grammars obtained by combining nonterminals to corresponding parentheses which can only be substituted simultaneously. Refering to the generative capacity of the grammars we obtain an infinite hierarchy of languages that comprises the context-free languages as the first and all the languages generated by TAGs as the second element. Here, we present a generalization of the context-free LL (k)-notion onto coupled-context-free grammars, which leads to a characterization of subclasses of coupled-context-free grammars-and in this way of TAGs as well-which can be parsed in linear time. The parsing procedure described works incrementally so that it can be used for on-line parsing of natural language. Examples show that important elements of the tree-adjoining languages can be generated by LL(k)-coupled-context-free grammars
6 citations
Proceedings Article•
01 Jan 1972
TL;DR: Context -sens i t ive g r a m m a r s in which each rule is of the forln a Z f l -~ (-*Tfl are acyclic if the associa ted context-free g r an in tmt s t r ing is in the language genera ted by an acYclic contextsensi.
Abstract: Context -sens i t ive g r a m m a r s in which each rule is of the forln a Z f l -~ (-*Tfl are acyclic if the associa ted context-free g r a m m a r wi th the rules Z ~ 3' is acyclic. The prob lem whe the r an in tmt s t r ing is in the language genera ted by an acyclic contextsensi t ive g r a m m a r is NP-conlple te .
6 citations
TL;DR: Some results on the power of external contextual grammars with regular commutative, regular circular, definite, suffix-free, ordered, combinational, nilpotent, and union-free selection languages are given.
6 citations