Regular expression for capturing a "C-style" string
Here is a regular expression for the set of all strings of the following form:


They start and end with ".
Every " in the middle must be escaped using a backslash.
Every backslash must be followed by a letter from $A$.
All other letters are from $B$; in particular, " is not in $B$.


For simplicity, I identify $A$ and $B$ with the regular expressions $\sum_{\sigma \in A} \sigma$ and $\sum_{\tau \in B} \tau$.

Here is the regular expression:
$$
\text"(B+\backslash A)^*\text"
$$