  Our aim is to construct a finite automaton recognizing the set of words that
are at a bounded distance from some word of a given regular language. We define
new regular operators, the similarity operators, based on a generalization of
the notion of distance and we introduce the family of regular expressions
extended to similarity operators, that we call AREs (Approximate Regular
Expressions). We set formulae to compute the Brzozowski derivatives and the
Antimirov derivatives of an ARE, which allows us to give a solution to the ARE
membership problem and to provide the construction of two recognizers for the
language denoted by an ARE. As far as we know, the family of approximative
regular expressions is introduced for the first time in this paper. Classical
approximate regular expression matching algorithms are approximate matching
algorithms on regular expressions. Our approach is rather to process an exact
matching on approximate regular expressions.
