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 article, it was shown that primitives and bases in free groups of rank higher than two are context-sensitive, and that primitive sets in the free group on two generators, the Bridson-Gilman normal forms for the fundamental groups of 3-manifolds or orbifolds, can be generated by L systems.
Abstract: L systems generalize context-free grammars by incorporating parallel rewriting, and generate languages such as EDT0L and ET0L that are strictly contained in the class of indexed languages. In this paper, we show that many of the languages naturally appearing in group theory, and that were known to be indexed or context-sensitive, are in fact ET0L and in many cases EDT0L. For instance, the language of primitives and bases in the free group on two generators, the Bridson–Gilman normal forms for the fundamental groups of 3-manifolds or orbifolds, and the co-word problem of Grigorchuk’s group can be generated by L systems. To complement the result on primitives in rank 2 free groups, we show that the language of primitives, and primitive sets, in free groups of rank higher than two is context-sensitive. We also show the existence of EDT0L languages of intermediate growth.
19 citations
TL;DR: It is proved in this note that the class of all languages recognized by 2pfa's is strictly included in theclass of all deterministic context-sensitive languages.
19 citations
TL;DR: A method for decomposing subclasses of different families of languages, parallel in nature, into other families, can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family.
Abstract: In this paper we give a method for decomposing subclasses of different families of languages, parallel in nature, into other families. These decomposition theorems can be used to produce languages not it a family by using examples of languages not belonging to some “smaller” family.
18 citations
TL;DR: The Bounded Context Parsable Grammars are defined, a class of recursive subsets of context free grammars for which the authors can construct linear time parsers and it is shown that the set of languages of thegrammars thus defined properly contains theSet of deterministic languages without the empty sentence.
Abstract: In this paper we extend Floyd's notion of parsing by bounded context to define the Bounded Context Parsable Grammars, a class of recursive subsets of context free grammars for which we can construct linear time parsers. It is shown that the set of languages of the grammars thus defined properly contains the set of deterministic languages without the empty sentence.
18 citations
04 Jul 2005
TL;DR: In a preceding paper, Bruyere and the second author introduced automata, as well as rational expressions, which allow to deal with words indexed by linear orderings, and this paper extends this result to languages of Words indexed by all linear ordering.
Abstract: In a preceding paper, Bruyere and the second author introduced automata, as well as rational expressions, which allow to deal with words indexed by linear orderings. A Kleene-like theorem was proved for words indexed by countable scattered linear orderings. In this paper we extend this result to languages of words indexed by all linear orderings.
18 citations