Paren n is the typical generalization of Dyck language to multiple types parentheses. We generalize its notion balancedness allow parentheses different freely commute. show that balanced regular and [Formula: see text]-regular languages can be characterized by syntactic constraints on expressions and, using shuffle trajectories operator, we define grammars for balanced-by-construction with whic...

We describe algorithms that directly infer regular expressions from positive data and characterize the regular language classes that can be learned this way.