Regular languages of partial words

We initiate a study of languages of partial words related to regular languages of full words. First, we investigate the possibility of expressing a regular language of full words as the image of a partial-words-language through a substitution that only replaces the hole symbols of the partial words by a finite set of letters. Results regarding the structure, uniqueness and succinctness of such a representation, as well as a series of related decidability and computational-hardness results, are presented. Finally, we introduce a hierarchy of classes of languages of partial words, by grouping together languages that can be connected in various strong ways to regular languages, and derive their closure properties with respect to several regular operations.