Regular closure of deterministic languages

We recall the notion of regular closure of classes of languages. We present two important results. The first result is that all languages which are in the regular closure of the class of deterministic (context-free) languages can be recognized in linear time. This is a nontrivial result, since this closure contains many inherently ambiguous languages. The second result is that the class of deterministic languages is contained in the closure of th e class of deterministic languages with the prefix property or, stated in a n equivalent way, all LR(k) languages are in the regular closure of the cla ss of LR(0) languages.