  This paper proposes an extension to classical regular expressions by the
addition of two operators allowing the inclusion of boolean formulae from the
zeroth order logic. These expressions are called constrained expressions. The
associated language is defined thanks to the notion of interpretation and of
realization.
  We show that the language associated when both interpretation and realization
are fixed is stricly regular and can be not regular otherwise.
  Furthermore, we use an extension of Antimirov partial derivatives in order to
solve the membership test in the general case. Finally, we show that once the
interpretation is fixed, the membership test of a word in the language denoted
by a constrained expression can be undecidable whereas it is always decidable
when the interpretation is not fixed.
