A class by principal congruence of a syntactically embedded language
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 I'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 Pw(m) class. From the above results, we can obtain those for principal congruence of some codes. For example, L-n is equal to a P-L(n-1) class for an inter code L of index n.
principal congruence inter code prefix code suffix code infix code conuna-free code