What I mean by a "symbolic regular expression" (if there already is a different name for this I'm not aware of it) is a regular expression that may include exponents that are symbolic arithmetic expressions.
Example 1: $a^k|b^*$ means "either $k$ copies of $a$ or zero or more copies of $b$".
Example 2: $a^{k+1}|a^k$ means "either $k$ or $k+1$ copies of $a$".
What I'd like to do is disambiguate such regular expressions. I know that to disambiguate a normal regular expression, you can convert it to an NFA, then a DFA, then back to a regular expression.
The problem is not completely straightforward. For example, $a^k|a^j$ is ambiguous if $j=k$ and unambiguous otherwise. Thus, the appropriate output would be, for example, $$a^k \text{ if } k=j, \qquad a^k|a^j \text{ otherwise.}$$
Does anyone know if there has been anything written about this problem?