A Class by Principal Congruence of a Syntactically Embedded Language

Tetsuo MORIYA  

IEICE TRANSACTIONS on Information and Systems   Vol.E90-D   No.6   pp.975-978
Publication Date: 2007/06/01
Online ISSN: 1745-1361
DOI: 10.1093/ietisy/e90-d.6.975
Print ISSN: 0916-8532
Type of Manuscript: LETTER
Category: Automata and Formal Language Theory
prefix code,  suffix code,  infix code,  comma-free code,  inter code,  principal congruence,  

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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 PL 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 PM class. (2) For a language K, s-embedded in an infix language M, K is equal to a PW(M) class. (3) For a nonempty s-embedded language L, if L is double-unitary, then L is equal to a PW(M) class. From the above results, we can obtain those for principal congruence of some codes. For example, Ln is equal to a PLn+1 class for an inter code L of index n.