Before revision:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems in the fields of constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.
After revision:  We demonstrate that, by applying our FPRAS for tree automata, we can obtain an FPRAS for many hitherto open problems , such as counting solutions to constraint satisfaction problems ( CSPs) , database systems, software verification, and knowledge compilation.