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(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.
| Original language | English |
|---|---|
| Pages (from-to) | 323-341 |
| Number of pages | 19 |
| Journal | Fundamenta Informaticae |
| Volume | 154 |
| Issue number | 1-4 |
| DOIs | |
| Publication status | Published - 2017 |
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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
Cite this
Morphic characterizations of language families based on local and star languages. / Okubo, Fumiya; Yokomori, Takashi.
In: Fundamenta Informaticae, Vol. 154, No. 1-4, 2017, p. 323-341.Research output: Contribution to journal › Article
}
TY - JOUR
T1 - Morphic characterizations of language families based on local and star languages
AU - Okubo, Fumiya
AU - Yokomori, Takashi
PY - 2017
Y1 - 2017
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
UR - http://www.scopus.com/inward/record.url?scp=85027304818&partnerID=8YFLogxK
UR - http://www.scopus.com/inward/citedby.url?scp=85027304818&partnerID=8YFLogxK
U2 - 10.3233/FI-2017-1569
DO - 10.3233/FI-2017-1569
M3 - Article
AN - SCOPUS:85027304818
VL - 154
SP - 323
EP - 341
JO - Fundamenta Informaticae
JF - Fundamenta Informaticae
SN - 0169-2968
IS - 1-4
ER -