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Showing papers on "Indexed language published in 1986"


Proceedings ArticleDOI
25 Aug 1986
TL;DR: It is shown that Head Languages are included in Tree Adjoining Languages and that Tree Adjoined Grammars are equivalent to a modification of Head Grammar called Modified Head GramMars.
Abstract: In this paper we discuss the formal relationship between thw classes of languages generated by Tree Adjoining Grammars and Head Grammars. In particular, we show that Head Languages are included in Tree Adjoining Languages and that Tree Adjoining Grammars are equivalent to a modification of Head Grammars called Modified Head Grammars. The inclusion of MHL in HL, and thus the equivalence of HG's and TAG's in the most general case remains to be established.

38 citations


Book ChapterDOI
Howard Straubing1
15 Jul 1986
TL;DR: An effective criterion for determining whether a given language has dot-depth 2 is conjecture and the condition is shown to be necessary in general, and sufficient for languages over a two-letter alphabet.
Abstract: This paper is a contribution to the problem of effectively determining the dot-depth of a star-free language, a problem in the theory of automata and formal languages with close connections to algebra and formal logic. We conjecture an effective criterion for determining whether a given language has dot-depth 2. The condition is shown to be necessary in general, and sufficient for languages over a two-letter alphabet. The condition involves a novel use of categories in the study of semigroup-theoretic problems.

32 citations


Proceedings ArticleDOI
10 Jul 1986
TL;DR: The absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity, and a class of grammars must be found which handles (context-sensitive) copying but not ( context-free) mirror images, suggesting that human linguistic processes use queues rather than stacks.
Abstract: The documentation of (unbounded-length) copying and cross-serial constructions in a few languages in the recent literature is usually taken to mean that natural languages are slightly context-sensitive. However, this ignores those copying constructions which, while productive, cannot be easily shown to apply to infinite sublanguages. To allow such finite copying constructions to be taken into account in formal modeling, it is necessary to recognize that natural languages cannot be realistically represented by formal languages of the usual sort. Rather, they must be modeled as families of formal languages or as formal languages with indefinite vocabularies. Once this is done, we see copying as a truly pervasive and fundamental process in human language. Furthermore, the absence of mirror-image constructions in human languages means that it is not enough to extend Context-free Grammars in the direction of context-sensitivity. Instead, a class of grammars must be found which handles (context-sensitive) copying but not (context-free) mirror images. This suggests that human linguistic processes use queues rather than stacks, making imperative the development of a hierarchy of Queue Grammars as a counterweight to the Chomsky Grammars. A simple class of Context-free Queue Grammars is introduced and discussed.

22 citations


Journal ArticleDOI
TL;DR: This paper reduces the problem to the emptiness problem for the class of indexed languages in the logarithmic space, indicating the exponential-time difficulty of the emptinessproblem for the indexed language.
Abstract: The class of indexed languages properly includes the class of context-free languages and is properly included in the class of context-dependent languages [1]. The emptiness problem (the problem of determining whether or not the given language is empty) is polynomial-time complete for the class of context-free languages and is undecidable for the class of context-dependent languages. The recognition problem (the problem, given a language L and word w, of determining whether or not w belongs to L) is polynomial-time complete for the class of context-free languages and is polynomialspace complete for the class of contextdependent languages. This paper shows that both the emptiness and recognition problems are exponential-time complete for the class of indexed languages. It is known in the pebble game [2] that the problem of determining whether or not the first player has the winning strategy is exponential-time complete. This paper reduces the problem to the emptiness problem for the class of indexed languages in the logarithmic space, indicating the exponential-time difficulty of the emptiness problem for the indexed language. Since Aho has shown that the problem can be answered in exponential time, the exponential-time completeness is shown. The exponential-time difficulty is also directly indicated from the fact that the emptiness problem is exponential-time complete. Consequently, the recognition problem is also exponential-time complete.

11 citations


Journal ArticleDOI
TL;DR: It is shown that non self-embedding (right- linear, linear) indexed languages are exactly the ( right-linear,linear)_context-free languages.

3 citations


Proceedings ArticleDOI
01 Feb 1986
TL;DR: Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage.
Abstract: Permission to copy without fee all or part of this material is granted provided that the copies are not made or distributed for direct commercial advantage, the ACM copyright notice and the title of the publication and its date appear, and notice is given that copying is by permission of the Association for Computing Machinery. To copy otherwise, or to republish, requires a fee and/or specific permission.

1 citations