What do you use it for?
One of the more famous places where these constraint solvers are used is to deal with dependency management in package systems. For example, zeroinstall uses a SAT solver to resolve dependency conflicts.
http://0install.net/solver.html
A sillier example is the time I used a sat solver to find the solutions for a flash puzzle game. The part I'm proudest of is that the sat solver could handle the highly symmetric cases that stumped the hand-written backtracking algorithms. And if I had used an SMT solver instead of SAT I would not have had to convert everything all the way doen to boolean formulas.
https://github.com/hugomg/hexiom
In the readme I explain a bit why the sat solver helped.
Would a SAT solver be useful for compiler technologies?
A compiler is basically solving the problem of: here is a sequence of things I want done; here is a description of what the machine can do; find a combination of the latter which achieves the former. The details are the tricky bit, particularly for unpleasantly asymmetric instruction sets like the old 8-bit architectures.
It would be so nice if I could just throw a description of the problem at some sort of machine reasoning system and have it Just Work...
But current SAT solvers aren't powerful enough to do so at much more than a few tens of instructions long. Still useful though.
Perhaps the most relevant example project here would be Rosette[4], which is basically a framework for easily writing synthesizers for different tasks. It would let you implement a description of your machine in Scheme (ie write a simple interpreter) and automatically generate a synthesizer for it that could compile programs in your language to formulas in a solver of some sort.
[1]: http://www.cs.berkeley.edu/~bodik/cs294/fa12/Lectures/L1/L1-...
[2]: http://jelv.is/chlorophyll.pdf
I'm afraid your paper is largely beyond me, though, but I'll go read up on program synthesis. Thanks!
It was tongue-in-cheek, I enjoyed the positivity in your original comment.