A language over a finite alphabet X is called disjunctive if the principal congruence PL determined by L is the equality. A dense language is a language which has non-empty intersection with any two-sided ideal of the free monoid X* generated by the alphabet X. We call an infinite language L completely disjunctive (completely dense) if every infinite
subset of L is disjunctive (dense). For a language L, if every dense subset of L is disjunctive, then we call L quasi-completely disjunctive. In this paper, (for the case IXI ≥ 2) we show that every completely disjunctive language is completely dense and conversely. Characterizations of completely disjunctive languages and quasi-completely disjunctive languages were obtained. We also discuss some operations on the families of languages.
Abstract This study extends the understanding of involution palindrome words. The involution is an antimorphic function concerning the Watson-Crick complementarity. Some algebraic properties of skew involution palindrome words and weak involution palindrome languages are studied. The characteristics of involution palindrome-preserving homomorphisms are also investigated in this paper. Keywords: Antimorphic involutionprimitive wordhomomorphism
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