Brüggemann-Klein and Wood have introduced a new family of regular languages, the
one-unambiguous regular languages
, a very important notion in XML DTDs. A regular language
is one-unambiguous if and only if there exists a regular expression
over the operators of sum, catenation and Kleene star such that
and the position automaton of
is deterministic. It implies that for a one-unambiguous expression, there exists an equivalent linear-size deterministic recognizer. In this paper, we extend the notion of one-unambiguity to weak one-unambiguity over regular expressions using the complement operator ¬. We show that a DFA with at most (
+ 2) states can be computed from a weakly one-unambiguous expression and that it is decidable whether or not a given DFA recognizes a weakly one-unambiguous language.