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: In this article, a distributed architecture based on cell-like P systems, with their skin membranes communicating through channels according to specified rules of the antiport type, where parts of a problem can be introduced as inputs in various components and then processed in parallel is considered.
Abstract: Although P systems are distributed parallel computing devices, no explicit way of handling the input in a distributed way in this framework was considered so far. This note proposes a distributed architecture (based on cell-like P systems, with their skin membranes communicating through channels as in tissue-like P systems, according to specified rules of the antiport type), where parts of a problem can be introduced as inputs in various components and then processed in parallel. The respective devices are called dP systems, with the case of accepting strings called dP automata. The communication complexity can be evaluated in various ways: statically (counting the communication rules in a dP system which solves a given problem), or dynamically (counting the number of communication steps, of communication rules used in a computation, or the number of objects communicated). For each measure, two notions of "parallelizability" can be introduced. Besides (informal) definitions, some illustrations of these idea are provided for dP automata: each regular language is "weakly parallelizable" (i.e., it can be recognized in this framework, using a constant number of communication steps), and there are languages of various types with respect to Chomsky hierarchy which are "efficiently parallelizable" (they are parallelizable and, moreover, are accepted in a faster way by a dP automaton than by a single P automaton). Several suggestions for further research are made.
57 citations
TL;DR: This article present an exposition of the theory of M-automata and G-automorphisms, or finite automata augmented with a multiply-only register storing an element of a given monoid or group.
Abstract: We present an exposition of the theory of M-automata and G-automata, or finite automata augmented with a multiply-only register storing an element of a given monoid or group. Included are a number of new results of a foundational nature. We illustrate our techniques with a group-theoretic interpretation and proof of a key theorem of Chomsky and Schutzenberger from formal language theory.
57 citations
27 Jun 2001
TL;DR: It is concluded that Minimalist Grammars are weakly equivalent to Multiple Context-Free Grammar.
Abstract: In this paper we will fix the position of Minimalist Grammars as defined in Stabler (1997) in the hierarchy of formal languages. Michaelis (1998) has shown that the set of languages generated by Minimalist Grammars is a subset of the set of languages generated by Multiple Context-Free Grammars (Seki et al., 1991). In this paper we will present a proof showing the reverse. We thus conclude that Minimalist Grammars are weakly equivalent to Multiple Context-Free Grammars.
56 citations
TL;DR: What is currently known about natural language morphology and syntax from the perspective of formal language theory is surveyed and recent developments such as feature-theory, the use of extension and unification, default mechanisms, and metagram-matical techniques are outlined.
Abstract: This paper surveys what is currently known about natural language morphology and syntax from the perspective of formal language theory. Firstly, the position of natural language word-sets and sentence-sets on the formal language hierarchy is discussed. Secondly, the contemporary use by linguists of a range of formal grammars (from finite state transducers to indexed grammars) in both word-syntax (i.e. morphology) and sentence-syntax is sketched. Finally, recent developments such as feature-theory, the use of extension and unification, default mechanisms, and metagram-matical techniques, are outlined.
55 citations
TL;DR: This paper proves the existence of a hierarchy of languages which is properly contained in the context sensitive languages and which starts with the context-free family, defined inductively by controlling labeled linear grammars with languages in one family to yield languages in the next larger family.
55 citations