scholarly journals Formal language theory: refining the Chomsky hierarchy

2012 ◽  
Vol 367 (1598) ◽  
pp. 1956-1970 ◽  
Author(s):  
Gerhard Jäger ◽  
James Rogers
Keyword(s):  
Natural Language ◽  
Formal Language ◽  
Regular Languages ◽  
Language Theory ◽  
Context Free Grammar ◽  
Chomsky Hierarchy ◽  
Context Sensitive ◽  
Four Levels ◽  
Context Free ◽  
Natural Language Syntax

The first part of this article gives a brief overview of the four levels of the Chomsky hierarchy, with a special emphasis on context-free and regular languages. It then recapitulates the arguments why neither regular nor context-free grammar is sufficiently expressive to capture all phenomena in the natural language syntax. In the second part, two refinements of the Chomsky hierarchy are reviewed, which are both relevant to the extant research in cognitive science: the mildly context-sensitive languages (which are located between context-free and context-sensitive languages), and the sub-regular hierarchy (which distinguishes several levels of complexity within the class of regular languages).

Context Free Grammar Identification from Positive Samples

2018 ◽  
Vol 7 (3.12) ◽  
pp. 1096
Author(s):  
K Senthil Kumar ◽  
D Malathi
Keyword(s):  
Formal Language ◽  
Target Language ◽  
Language Theory ◽  
Grammatical Inference ◽  
Context Free Grammar ◽  
Chomsky Hierarchy ◽  
Compiler Design ◽  
Novel Method ◽  
Context Free

In grammatical inference one aims to find underlying grammar or automaton which explains the target language in some way. Context free grammar which represents type 2 grammar in Chomsky hierarchy has many applications in Formal Language Theory, pattern recognition, Speech recognition, Machine learning , Compiler design and Genetic engineering etc. Identification of unknown Context Free grammar of the target language from positive examples is an extensive area in Grammatical Inference/ Grammar induction. In this paper we propose a novel method which finds the equivalent Chomsky Normal form.  

scholarly journals Derivation "Trees" and Parallelism in Chomsky-Type Grammars

Triangle ◽  
2018 ◽  
pp. 101
Author(s):  
Benedek Nagy
Keyword(s):  
Formal Language ◽  
Phrase Structure ◽  
Formal Language Theory ◽  
Language Theory ◽  
Context Sensitive ◽  
Recursively Enumerable ◽  
Rule Set ◽  
Context Free ◽  
Recursively Enumerable Languages ◽  
Context Free Grammars

In this paper we discuss parallel derivations for context-free, contextsensitive and phrase-structure grammars. For regular and linear grammars only sequential derivation can be applied, but a kind of parallelism is present in linear grammars. We show that nite languages can be generated by a recursion-free rule-set. It is well-known that in context-free grammars the derivation can be in maximal (independent) parallel way. We show that in cases of context-sensitive and recursively enumerable languages the parallel branches of the derivation have some synchronization points. In the case of context-sensitive grammars this synchronization can only be local, but in a derivation of an arbitrary grammar we cannot make this restriction. We present a framework to show how the concept of parallelism can be t to the derivations in formal language theory using tokens.

Formal Grammars and Languages

2012 ◽  
Author(s):  
Carlos Martín-Vide
Keyword(s):  
Systematic Study ◽  
Formal Language ◽  
Formal Language Theory ◽  
Language Theory ◽  
Context Free Grammar ◽  
Formal Grammars ◽  
The Common ◽  
Context Free ◽  
The Way

This article introduces the preliminaries of classical formal language theory. It outlines the main classes of grammars as language-generating devices and automata as language-recognizing devices. It offers a number of definitions and examples and presents the basic results. It classifies grammar according to several criteria. The most widespread one is the form of their productions. This article presents a systematic study of the common properties of language families has led to the theory of abstract families of languages. It shows that a context-free grammar generates not only a set of strings, but a set of trees too: each one of the trees is associated with a string and illustrates the way this string is derived in the grammar.

scholarly journals Phonological typology in Optimality Theory and Formal Language Theory: goals and future directions

Phonology ◽  
2019 ◽  
Vol 36 (2) ◽  
pp. 351-353
Author(s):  
Joe Pater
Keyword(s):  
Recent Work ◽  
Optimality Theory ◽  
Formal Language ◽  
Regular Languages ◽  
Formal Language Theory ◽  
Language Theory ◽  
Future Directions ◽  
Chomsky Hierarchy ◽  
Phonological Typology

Much recent work has studied phonological typology in terms of Formal Language Theory (e.g. the Chomsky hierarchy). This paper considers whether Optimality Theory grammars might be constrained to generate only regular languages, and also whether the tools of formal language theory might be used for constructing phonological theories similar to those within Optimality Theory. It offers reasons to be optimistic about the first possibility, and sceptical about the second.

scholarly journals Principles of structure building in music, language and animal song

2015 ◽  
Vol 370 (1664) ◽  
pp. 20140097 ◽  
Author(s):  
Martin Rohrmeier ◽  
Willem Zuidema ◽  
Geraint A. Wiggins ◽  
Constance Scharff
Keyword(s):  
Formal Language ◽  
Animal Communication ◽  
Structural Complexity ◽  
Language Theory ◽  
Human Language ◽  
Chomsky Hierarchy ◽  
Structure Building ◽  
Animal Vocalizations ◽  
Communicative Success ◽  
Parallel Feature

Human language, music and a variety of animal vocalizations constitute ways of sonic communication that exhibit remarkable structural complexity. While the complexities of language and possible parallels in animal communication have been discussed intensively, reflections on the complexity of music and animal song, and their comparisons, are underrepresented. In some ways, music and animal songs are more comparable to each other than to language as propositional semantics cannot be used as indicator of communicative success or wellformedness, and notions of grammaticality are less easily defined. This review brings together accounts of the principles of structure building in music and animal song. It relates them to corresponding models in formal language theory, the extended Chomsky hierarchy (CH), and their probabilistic counterparts. We further discuss common misunderstandings and shortcomings concerning the CH and suggest ways to move beyond. We discuss language, music and animal song in the context of their function and motivation and further integrate problems and issues that are less commonly addressed in the context of language, including continuous event spaces, features of sound and timbre, representation of temporality and interactions of multiple parallel feature streams. We discuss these aspects in the light of recent theoretical, cognitive, neuroscientific and modelling research in the domains of music, language and animal song.

scholarly journals REPRESENTATIONS AND CHARACTERIZATIONS OF LANGUAGES IN CHOMSKY HIERARCHY BY MEANS OF INSERTION-DELETION SYSTEMS

2008 ◽  
Vol 19 (04) ◽  
pp. 859-871 ◽  
Author(s):  
GHEORGHE PĂUN ◽  
MARIO J. PÉREZ-JIMÉNEZ ◽  
TAKASHI YOKOMORI
Keyword(s):  
Dna Computing ◽  
Research Direction ◽  
Regular Languages ◽  
Turing Computability ◽  
Chomsky Hierarchy ◽  
Recursively Enumerable ◽  
Enumerable Language ◽  
Language L ◽  
Context Free

Insertion-deletion operations are much investigated in linguistics and in DNA computing and several characterizations of Turing computability and characterizations or representations of languages in Chomsky hierarchy were obtained in this framework. In this note we contribute to this research direction with a new characterization of this type, as well as with representations of regular and context-free languages, mainly starting from context-free insertion systems of as small as possible complexity. For instance, each recursively enumerable language L can be represented in a way similar to the celebrated Chomsky-Schützenberger representation of context-free languages, i.e., in the form L = h(L(γ) ∩ D), where γ is an insertion system of weight (3, 0) (at most three symbols are inserted in a context of length zero), h is a projection, and D is a Dyck language. A similar representation can be obtained for regular languages, involving insertion systems of weight (2,0) and star languages, as well as for context-free languages – this time using insertion systems of weight (3, 0) and star languages.

scholarly journals Digraph complexity measures and applications in formal language theory

2012 ◽  
Vol Vol. 14 no. 2 (Automata, Logic and Semantics) ◽  
Author(s):  
Hermann Gruber
Keyword(s):  
Polynomial Time ◽  
Formal Language ◽  
Regular Languages ◽  
Formal Language Theory ◽  
Language Theory ◽  
Complexity Measures ◽  
Time Approximation ◽  
Np Complete ◽  
Cycle Rank ◽  
Polynomial Time Approximation

Automata, Logic and Semantics International audience We investigate structural complexity measures on digraphs, in particular the cycle rank. This concept is intimately related to a classical topic in formal language theory, namely the star height of regular languages. We explore this connection, and obtain several new algorithmic insights regarding both cycle rank and star height. Among other results, we show that computing the cycle rank is NP-complete, even for sparse digraphs of maximum outdegree 2. Notwithstanding, we provide both a polynomial-time approximation algorithm and an exponential-time exact algorithm for this problem. The former algorithm yields an O((log n)^(3/2))- approximation in polynomial time, whereas the latter yields the optimum solution, and runs in time and space O*(1.9129^n) on digraphs of maximum outdegree at most two. Regarding the star height problem, we identify a subclass of the regular languages for which we can precisely determine the computational complexity of the star height problem. Namely, the star height problem for bideterministic languages is NP-complete, and this holds already for binary alphabets. Then we translate the algorithmic results concerning cycle rank to the bideterministic star height problem, thus giving a polynomial-time approximation as well as a reasonably fast exact exponential algorithm for bideterministic star height.

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