# Bounds on the construction of regular expressions' intersection operator

There are references on the exponential worst-case of the intersection operator for regular expressions (see [1]). However, I was wondering if there are similar results for the construction process itself?

Concretely, given two regular expressions $$E_1$$ and $$E_2$$ whose intersection can be represented by a regular expression of polynomial size, is the construction process itself bounded by exponential time or memory in the worst-case?

• Are you aware of the problem of minimizing a regex? – plshelp Aug 28 '20 at 11:40
• – plshelp Aug 28 '20 at 11:51
• @plshelp thanks for the links! Could you elaborate a bit more on how do they imply an answer to my question? I don't quite see the reduction. – user59861 Aug 31 '20 at 8:44