Backward Symbolic Execution with Loop Folding

Symbolic execution is an established program analysis technique that aims to search all possible execution paths of the given program. Due to the so-called path explosion problem, symbolic execution is usually unable to analyze all execution paths and thus it is not convenient for program verification as a standalone method. This paper focuses on backward symbolic execution (BSE), which searches program paths backwards from the error location whose reachability should be proven or refuted. We show that this technique is equivalent to performing k-induction on control-flow paths. While standard BSE simply unwinds all program loops, we present an extension called loop folding that aims to derive loop invariants during BSE that are sufficient to prove the unreachability of the error location. The resulting technique is called backward symbolic execution with loop folding (BSELF). Our experiments show that BSELF performs better than BSE and other tools based on k-induction when non-trivial benchmarks are considered. Moreover, a sequential combination of symbolic execution and BSELF achieved very competitive results compared to state-of-the-art verification tools.