Topic
Chomsky hierarchy
About: Chomsky hierarchy is a research topic. Over the lifetime, 601 publications have been published within this topic receiving 31067 citations. The topic is also known as: Chomsky–Schützenberger hierarchy.
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TL;DR: It is shown that any recursively enumerable language can be characterized by the homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 5.
Abstract: In this work we initiate the study of Szilard languages of labelled insertion grammars. It is well-known that there exist context-free languages which cannot be generated by any insertion grammar. We show that there exist some regular languages which cannot be Szilard language of any labelled insertion grammar. But any regular language can be given as a homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 1. Also, any context-free language can be obtained as a homomorphic image of Szilard language of a labelled insertion grammar of weight 2. We show that even though insertion grammars of weight 1 can generate only context-free languages, there exist some context-sensitive language which can be obtained as Szilard language of a labelled insertion grammar of weight 1. At the end we show that any recursively enumerable language can be characterized by the homomorphic image of Szilard language obtained by a labelled insertion grammar of weight 5.
2 citations
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TL;DR: It is shown that the classes of languages obtained in this way are recognizable in polynomial time provided that all components of the pattern interpretation are injective homomorphisms.
Abstract: A word w is obtained by an ordered n-pattern interpretation of a word x if there are n homomorphisms h
1,h2,ċċċ, hn such that w=h1(x)h2(x)ċs hn(x). This ordered multiple pattern interpretation is naturally extended to languages. We show a strong relationship between the family of languages obtained by ordered multiple pattern interpretations of regular, linear, and context-free languages and the family of regular, linear, and context-free simple matrix languages. Concepts of ambiguity and inherent ambiguity of ordered multiple pattern interpretation are defined and it is shown that these properties are not decidable on the class of context-free languages. Then, we investigate arbitrary multiple pattern interpretations of the same classes of languages in the Chomsky hierarchy. We show that the classes of languages obtained in this way are recognizable in polynomial time provided that all components of the pattern interpretation are injective homomorphisms. We also present a series of open problems.
2 citations
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TL;DR: A hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family.
Abstract: This paper defines a hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context free family. The hierarchy is defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family. The families of the hierarchy have properties analogous to those of the context free family, in particular, the new mechanism introduced is very suitable for parsing.
A language in the n-th family is specified by a sequence of n -- 1 labeled linear grammars and a context free grammar. By assuming that the reversals of the first n -- 1 grammars and the last labeled linear grammar are precedence grammars, the concepts and parsing algorithm of Wirth and Weber extend to yield a parsing algorithm within the hierarchy. This considerably enhances the usefulness of the construction and allows much of the power of the context sensitive languages to become accessible in measured amounts for potential programming applications.
2 citations
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TL;DR: It is shown that, given a right linear or a strongLL(k) grammar, it is possible to produce automatically a pointer Markov algorithm parsing the language generated by the grammar.
Abstract: Markov algorithms have received very little attention in the studies about formal languages, so the purpose of the present paper is twofold: i) to characterize languages in terms of Markov algorithms, and ii) to produce automatically Markov algorithms accepting or parsing languages generated by given grammars.
2 citations