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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7 citations
14 Nov 1988
TL;DR: It is shown that only regular languages belong to the same levels of both hierarchies, which implies that VLSI circuits need Θ (n) area and Θ(n2) area to recognize deterministic context-free languages.
Abstract: Chomsky hierarchy is compared with the hierarchy of communication complexity for VLSI. It is shown that only regular languages belong to the same levels of both hierarchies. There are hard languages according to Chomsky hierarchy that belong to the lowest level in communication complexity hierarchy. On the other hand there is a deterministic linear language that requires the highest (linear) communication complexity. This is the main result because it implies that VLSI circuits need Θ(n) area and Θ(n2) area. (time)2 complexity to recognize deterministic context-free languages which solves an open problem of Hromkovic [7].
7 citations
26 Jun 2006
TL;DR: In this article, the expressive power of the boolean closures of GCSL, CRL, CFL, and LOGCFL is investigated, and it is shown that there exists an infinite intersection hierarchy.
Abstract: The class of growing context-sensitive languages (GCSL) is a naturally defined subclass of context-sensitive languages whose membership problem is solvable in polynomial time. GCSL and its deterministic counterpart called Church-Rosser Languages (CRL) complement the Chomsky hierarchy in a natural way [9]. In this paper, the extension of GCSL obtained by closures of this class under the boolean operations are investigated. We show that there exists an infinite intersection hierarchy, answering an open problem from [1]. Further, we compare the expressive power of the boolean closures of GCSL, CRL, CFL and LOGCFL.
7 citations
TL;DR: It is proved that the class of polynomial measurable languages is a Pre-AFL, which is a special case of the general notion.
Abstract: In this paper we introduce a class of measures on formal languages. These measures are based on the number of different ways a string of a specified finite length can be completed to obtain strings of the language. The relation with automata and grammars is established, and the polynomial measure, a special case of the general notion, is studied in detail. We give some closure properties for well-known operations on languages, and finally, we prove that the class of polynomial measurable languages is a Pre-AFL.
7 citations
Journal Article•
TL;DR: A survey on the various models of restarting automata and their properties is given, their relationships to the language classes of the Chomsky hierarchy are described, and some open problems are presented.
Abstract: The restarting automaton, introduced by Jancar et al in 1995, is motivated by the so-called 'analysis by reduction,' a technique from linguistics. By now there are many different models of restarting automata, and their investigation has proved very fruitful in that they offer an opportunity to study the influence of various kinds of resources on their expressive power. Here a survey on the various models and their properties is given, their relationships to the language classes of the Chomsky hierarchy are described, and some open problems are presented.
7 citations