P S $$\mathcal {P}\mathcal {S}$$ -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 8 in Topics on Combinatorial Semigroups, 2024, pp 237-260 from Springer

Abstract: Abstract In this chapter, by using “permissible subsets”, we obtain a kind of generalized principal congruences determined by languages. Applying this kind of generalized principal congruences, we introduce and investigate a class of generalized regular languages, namely, P S $$\mathcal {P}\mathcal {S}$$ -regular languages. We give some characterizations of such generalized regular languages. As applications of the results, we obtain some characterizations of regular languages. Also, we consider the closure properties of the class of P S $$\mathcal {P}\mathcal {S}$$ -regular languages, and the relationship among P S $$\mathcal {P}\mathcal {S}$$ -regular languages, context-free languages and context-sensitive languages. As usual, A is always a finite alphabet throughout this chapter.

Date: 2024
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DOI: 10.1007/978-981-99-9171-6_8

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