Abstract
In this paper a formalism is proposed, named fair expressions, partly introduced in [Bre94], that extends regular expressions to lists, having strings as components. This formalism uses classical regular operators, i.e. catenation and its closure, and novel ones, namely the operator of merge and its closure, which are natural for lists. Fair expressions allow to define languages of lists, named fair languages, which can be compared to word languages by flattening the lists into strings. In this paper the basic properties of fair languages are briefly summarized and also extended with respect to previous works [Bre94]: hierarchy, semilinearity, closure, decidability and comparison with the Chomsky hierarchy are dealt with. The family offair languages is however far larger than the regular one; as a novel contribution this paper investigates its subfamilies that are comparable with regular languages. The main result that the regular subfamilies offair languages constitute a proper hierarchy. These subfamilies are then characterized and their properties are explored, showing that they are, in general, more mathematically tractable than fair languages. The conclusion lists comparisons with related works, open problems and research directions.
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