Morphic characterizations of language families based on local and star languages

Fumiya Okubo; Takashi Yokomori

doi:10.3233/FI-2017-1569

Morphic characterizations of language families based on local and star languages

Fumiya Okubo, Takashi Yokomori

Research output: Contribution to journal › Article › peer-review

3 Citations (Scopus)

Abstract

New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(T_k ∩ F_R) for some 2-star language F_R, an extended 2-star language T_k and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(D_n ∩ F_L) for some 2-local language F_L and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language F_L and a weak coding h such that L = h(B_n ∩ F_L), where D_n and B_n are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

Original language	English
Pages (from-to)	323-341
Number of pages	19
Journal	Fundamenta Informaticae
Volume	154
Issue number	1-4
DOIs	https://doi.org/10.3233/FI-2017-1569
Publication status	Published - 2017

Keywords

Chemical reaction automata
Context-free languages
Local languages
Morphic characterizations
Regular languages
Star languages

ASJC Scopus subject areas

Theoretical Computer Science
Algebra and Number Theory
Information Systems
Computational Theory and Mathematics

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title = "Morphic characterizations of language families based on local and star languages",

abstract = "New morphic characterizations in the form of a noted Chomsky-Sch{\"u}tzenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.",

keywords = "Chemical reaction automata, Context-free languages, Local languages, Morphic characterizations, Regular languages, Star languages",

author = "Fumiya Okubo and Takashi Yokomori",

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AU - Okubo, Fumiya

AU - Yokomori, Takashi

PY - 2017

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N2 - New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

AB - New morphic characterizations in the form of a noted Chomsky-Schützenberger theorem are established for the classes of regular languages, of context-free languages and of languages accepted by chemical reaction automata. Our results include the following: (i) Each λ-free regular language R can be expressed as R = h(Tk ∩ FR) for some 2-star language FR, an extended 2-star language Tk and a weak coding h. (ii) Each λ-free context-free language L can be expressed as L = h(Dn ∩ FL) for some 2-local language FL and a projection h. (iii) A language L is accepted by a chemical reaction automaton iff there exist a 2-local language FL and a weak coding h such that L = h(Bn ∩ FL), where Dn and Bn are a Dyck set and a partially balanced language defined over the n-letter alphabet, respectively. These characterizations improve or shed new light on the previous results.

KW - Chemical reaction automata

KW - Context-free languages

KW - Local languages

KW - Morphic characterizations

KW - Regular languages

KW - Star languages

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Morphic characterizations of language families based on local and star languages

Abstract

Keywords

ASJC Scopus subject areas

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