We study regular expressions that use variables, or parameters, which are
interpreted as alphabet letters. We consider two classes of languages denoted
by such expressions: under the possibility semantics, a word belongs to the
language if it is denoted by some regular expression obtained by replacing
variables with letters; under the certainly semantics, the word must be denoted
by every such expression. Such languages are regular, and we show that they
naturally arise in several applications such as querying graph databases and
program analysis. As the main contribution of the paper, we provide a complete
characterization of the complexity of the main computational problems related
to such languages: nonemptiness, universality, containment, membership, as well
as the problem of constructing NFAs capturing such languages. We also look at
the extension when domains of variables could be arbitrary regular languages,
and show that under the certainty semantics, languages remain regular and the
complexity of the main computational problems does not change
