Symbolic execution is an effective program analysis technique whose scalability largely depends on the ability to quickly solve large numbers of first-order logic queries. We propose an effective general technique for speeding up the solving of queries in the theory of arrays and bit-vectors with a specific structure, while otherwise falling back to a complete solver.

The technique has two stages: a learning stage that determines the solution sets of each symbolic variable, and a decision stage that uses this information to quickly determine the satisfiability of certain types of queries. The main challenges involve deciding which operators to support and precisely dealing with integer type casts and arithmetic underflow and overflow.

We implemented this technique in an incomplete solver called PARTI (``PARtial Theory solver for Intervals''), directly integrating it into the popular KLEE symbolic execution engine. We applied KLEE with PARTI and a state-of-the-art SMT solver to synthetic and real-world benchmarks. We found that PARTI practically does not hurt performance while many times achieving order-of-magnitude speedups.