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IEICE TRANSACTIONS on Information

Homomorphic Characterizations Are More Powerful Than Dyck Reductions

Sadaki HIROSE, Satoshi OKAWA, Haruhiko KIMURA

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Summary :

Let L be any class of languages, L' be a class of languages which is closed under λ-free homomorphisms, and Σ be any alphabet. In this paper, we show that if the following statement (1) holds, then the statement (2) holds. (1) For any language L in L over Σ, there exist an alphabet of k pairs of matching parentheses Xk, Dyck reduction Red over Xk, and a language L1 in L' over ΣXk such that L=Red(L1)Σ*. (2) For any language L in L over Σ, there exist an alphabet Γ including Σ, a homomorphism h : Γ*Σ*, a Dyck language D over Γ, and a language L2 in L' over Γ such that L=h(DL2). We also give an application of this result.

Publication
IEICE TRANSACTIONS on Information Vol.E80-D No.3 pp.390-392
Publication Date
1997/03/25
Publicized
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DOI
Type of Manuscript
Category
Automata,Languages and Theory of Computing

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