Relatively Disjunctive Languages and Relatively Regular Languages

Yuqi Guo, Yun Liu and Shoufeng Wang
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Yuqi Guo: Lanzhou University, School of Mathematics and Statistics
Yun Liu: Yuxi Normal University, Department of Mathematics
Shoufeng Wang: Yunnan Normal University, Department of Mathematics

Chapter Chapter 6 in Topics on Combinatorial Semigroups, 2024, pp 173-196 from Springer

Abstract: Abstract In this chapter, we will investigate relatively regular languages and relatively disjunctive languages systematically. The two classes of languages are natural generalizations of regular languages and disjunctive languages respectively and relatively disjunctive languages are even a generalization of f-disjunctive languages discussed in the previous chapter. One of the main results of the chapter is that “In any finite alphabet, all languages are divided into two disjoint classes: relatively regular languages and relatively disjunctive languages”. This is a natural generalization of the classification of languages on one-letter alphabets, and in some sense, gives a corresponding classification of languages on finite alphabets.

Date: 2024
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DOI: 10.1007/978-981-99-9171-6_6

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