A challenging problem in symbolic execution is to solve complex mathematical constraints such as constraints that include floating-point variables and transcendental functions. The inability to solve such constraints limit the application scope of symbolic execution. In this paper, we present a new method to solve such complex math constraints. Our method combines two existing: meta-heuristic search and interval solving. Conceptually, the combination explores the synergy of the individual methods to improve constraint solving. We implemented the new method in the CORAL constraint-solving infrastructure, and evaluated its effectiveness on a set of publicly-available software from the aerospace domain. Results indicate that the new method can solve significantly more complex mathematical constraints than previous techniques.

We describe an approach to testing complex safety critical software that combines unit-level symbolic execution and system-level concrete execution for generating test cases that satisfy user-specified testing criteria. We have developed Symbolic Java PathFinder, a symbolic execution framework that implements a non-standard bytecode interpreter on top of the Java PathFinder model checking tool. The framework propagates the symbolic information via attributes associated with the program data. Furthermore, we use two techniques that leverage system-level concrete program executions to gather information about a unit's input to improve the precision of the unit-level test case generation. We applied our approach to testing a prototype NASA flight software component. Our analysis helped discover a serious bug that resulted in design changes to the software. Although we give our presentation in the context of a NASA project, we believe that our work is relevant for other critical systems that require thorough testing.