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

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.

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Digraph complexity measures and applications in formal language theory

Discrete Mathematics & Theoretical Computer Science ◽

10.46298/dmtcs.583 ◽

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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Formal language theory: refining the Chomsky hierarchy

Philosophical Transactions of the Royal Society B Biological Sciences ◽

10.1098/rstb.2012.0077 ◽

2012 ◽

Vol 367 (1598) ◽

pp. 1956-1970 ◽

Cited By ~ 57

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).

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A Note on Weak vs. Strong Generation in Human Language

Studies in Chinese Linguistics ◽

10.1515/scl-2015-0004 ◽

2015 ◽

Vol 36 (2) ◽

pp. 59-68 ◽

Cited By ~ 2

Author(s):

Naoki Fukui

Keyword(s):

Formal Language ◽

Formal Language Theory ◽

Language Theory ◽

Human Language ◽

Language Faculty ◽

Brain Science ◽

Chomsky Hierarchy ◽

Human Language Faculty

Abstract This paper argues that various important results of formal language theory (e.g., the so-called Chomsky Hierarchy) may in fact be illusory as far as the human language faculty is concerned, as has been repeatedly emphasized by Chomsky himself. The paper takes up nested dependencies and cross-serial dependencies, the two important dependencies that typically show up in the discussion of the central classes of grammars and languages, and specifically shows that the fact that nested dependencies abound in human language while cross-serial dependencies are rather limited in human language can be naturally explained if we shift our attention from dependencies defined on terminal strings to abstract structures behind them. The paper then shows that nested dependencies are readily obtained by Merge, applying phase-by-phase, whereas cross-serial dependencies are available only as a result of copying Merge, which requires a constituency of the relevant strings. These results strongly suggest that dependencies are possible in human language only to the extent that they are the results from the structures that can be generated by Merge, leading to the conclusion that it is Merge-generability that determines various dependencies in human language, and that dependencies defined on the terminal strings are indeed illusory. A possible brain science experiment to demonstrate this point is also suggested.

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Static Watson-Crick regular grammar

Malaysian Journal of Fundamental and Applied Sciences ◽

10.11113/mjfas.v14n0.1282 ◽

2018 ◽

Vol 14 ◽

pp. 457-462

Author(s):

Aqilahfarhana Abdul Rahman ◽

Wan Heng Fong ◽

Nor Haniza Sarmin ◽

Sherzod Turaev ◽

Nurul Liyana Mohamad Zulkufli

Keyword(s):

Dna Computing ◽

Formal Language ◽

Computational Models ◽

Formal Language Theory ◽

Language Theory ◽

Chomsky Hierarchy ◽

New Variant ◽

Sticker System ◽

Dna Strands ◽

Regular Grammar

DNA computing, or more generally, molecular computing, is a recent development at the interface of computer science and molecular biology. In DNA computing, many computational models have been proposed in the framework of formal language theory and automata such as Watson-Crick grammars and sticker systems. A Watson-Crick grammar is a grammar model that generates double stranded strings, whereas a sticker system is a DNA computing model of the ligation and annealing operations over DNA strands using the Watson-Crick complementarity to form a complete double stranded DNA sequence. Most of the proposed DNA computing models make use of this concept, including the Watson-Crick grammars and sticker systems. Watson-Crick grammars and their variants can be explored using formal language theory which allows the development of new concepts of Watson-Crick grammars. In this research, a new variant of Watson-Crick grammar called a static Watson-Crick regular grammar is introduced as an analytical counterpart of sticker systems. The computation of a sticker system starts from a given set of incomplete double stranded sequence to form a complete double stranded sequence. Here, a static Watson-Crick regular grammar differs from a dynamic Watson-Crick regular grammar in generating double stranded strings: the latter grammar produces each strand string “independently” and only check for the Watson-Crick complementarity of a generated complete double stranded string at the end, while the former grammar generates both strand strings “dependently”, i.e., checking for the Watson-Crick complementarity for each complete substring. In this paper, computational properties of static Watson-Crick regular grammars are investigated to correlate with the Chomsky hierarchy and hierarchy of the families of dynamic Watson-Crick regular languages. The relationship between families of languages generated by static Watson-Crick regular grammars with several variants of sticker systems, Watson-Crick regular grammars and Chomsky grammars are presented by showing the hierarchy.

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THE DEVELOPMENT OF FORMAL LANGUAGE THEORY SINCE 1956

International Journal of Foundations of Computer Science ◽

10.1142/s0129054190000254 ◽

1990 ◽

Vol 01 (04) ◽

pp. 355-368

Author(s):

ROBERT McNAUGHTON

Keyword(s):

Formal Language ◽

Formal Languages ◽

Early Years ◽

Formal Language Theory ◽

Language Theory ◽

Personal Interest

This brief survey will discuss the early years of the theory of formal languages through about 1970, treating only the most fundamental of the concepts. The paper will conclude with a brief discussion of a small number of topics, the choice reflecting only the personal interest of the author.

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