Parenn is the typical generalization of the Dyck language to multiple types of parentheses. We generalize its notion of balancedness to allow parentheses of different types to freely commute. We show that balanced regular and ω-regular languages can be characterized by syntactic constraints on regular and ω-regular expressions and, using the shuffle on trajectories operator, we define grammars for balanced-by-construction expressions with which one can express every balanced regular and ω-regular language.

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International Journal of Foundations of Computer Science
Centrum Wiskunde & Informatica, Amsterdam (CWI), The Netherlands

Edixhoven, L., & Jongmans, S. (2022). Balanced-by-Construction regular and ω-Regular languages. International Journal of Foundations of Computer Science. doi:10.1142/S0129054122440026