For Augeas, I needed a library to perform certain operations on regular languages, not just regular expressions. For example, Augeas needs to decide if two regular languages have words in common. Computations like these require working with finite automata, one of the theoretical underpinnings of regular expressions.
Sadly, there does not seem to be a well-maintained open source C library out there. That forced me to write my own. Luckily, there is a very good automata library written in Java: dk.brics.automaton. libfa is largely a reimplementation in C.
To save others from the pain I had to go through, libfa is built into a separate DSO when you build Augeas. To download it, download and install Augeas. It's not distributed separately, but if there's interest, I am more than happy to make that so.
When you install Augeas, libfa is installed as libfa.so, and the header file fa.h is put into /usr/include.
The source for libfa is in the files src/fa.[ch] in the Augeas sources. See Operations or fa.h for details on the operations supported by libfa.
Just like Augeas, libfa is licensed under the LGPL, version 2 or later.