A Class by Principal Congruence of a Syntactically Embedded Language

Tetsuo MORIYA

doi:10.1093/ietisy/e90-d.6.975

A Class by Principal Congruence of a Syntactically Embedded Language

Tetsuo MORIYA

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In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where P_L is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a P_M class. (2) For a language K, s-embedded in an infix language M, K is equal to a P_W(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a P_W(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Lⁿ is equal to a P_Lⁿ⁺¹ class for an inter code L of index n.

Publication: IEICE TRANSACTIONS on Information Vol.E90-D No.6 pp.975-978

Publication Date: 2007/06/01

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Online ISSN: 1745-1361

DOI: 10.1093/ietisy/e90-d.6.975

Type of Manuscript: LETTER

Category: Automata and Formal Language Theory

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Tetsuo MORIYA, "A Class by Principal Congruence of a Syntactically Embedded Language" in IEICE TRANSACTIONS on Information, vol. E90-D, no. 6, pp. 975-978, June 2007, doi: 10.1093/ietisy/e90-d.6.975.
Abstract: In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where P_L is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a P_M class. (2) For a language K, s-embedded in an infix language M, K is equal to a P_W(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a P_W(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Lⁿ is equal to a P_Lⁿ⁺¹ class for an inter code L of index n.
URL: https://global.ieice.org/en_transactions/information/10.1093/ietisy/e90-d.6.975/_p

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@ARTICLE{e90-d_6_975,
author={Tetsuo MORIYA, },
journal={IEICE TRANSACTIONS on Information},
title={A Class by Principal Congruence of a Syntactically Embedded Language},
year={2007},
volume={E90-D},
number={6},
pages={975-978},
abstract={In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where P_L is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a P_M class. (2) For a language K, s-embedded in an infix language M, K is equal to a P_W(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a P_W(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Lⁿ is equal to a P_Lⁿ⁺¹ class for an inter code L of index n.},
keywords={},
doi={10.1093/ietisy/e90-d.6.975},
ISSN={1745-1361},
month={June},}

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TY - JOUR
TI - A Class by Principal Congruence of a Syntactically Embedded Language
T2 - IEICE TRANSACTIONS on Information
SP - 975
EP - 978
AU - Tetsuo MORIYA
PY - 2007
DO - 10.1093/ietisy/e90-d.6.975
JO - IEICE TRANSACTIONS on Information
SN - 1745-1361
VL - E90-D
IS - 6
JA - IEICE TRANSACTIONS on Information
Y1 - June 2007
AB - In this paper, we introduce a syntactically embedded (s-embedded) language, and consider its principal congruence. The following three results are proved, where P_L is the principal congruence of a language L, and W(L) is the residual of L. (1) For a language K, s-embedded in M, K is equal to a P_M class. (2) For a language K, s-embedded in an infix language M, K is equal to a P_W(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a P_W(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Lⁿ is equal to a P_Lⁿ⁺¹ class for an inter code L of index n.
ER -