The common types of computational problems that I can find seems to be the following: decision problems, search problems, counting problems, optimization problems, and function problems.
For decision and search we have specialized tools for them, like SMT solvers. For optimization problems we also have constraint solving languages and tools. For special classes of function problems we also have things like computer algebra systems to solve them.
However we don't seem to have specialized automatic solving tools for counting problems. Why is it?
And are there any examples of computational problems that don't belong to any of these types?
