Today's software systems are often implicitly organized around enormous and complexly-structured design, construction, and usage spaces. This research focuses on defining, creating, and analyzing explicit models that link development spaces to the resulting test spaces underlying software development projects. The research will create and evaluate a new framework for testing systems with large and complex test spaces that (1) explicitly models a system's test space(s), (2) creates sophisticated algorithms that aggressively sample points in the test space, (3) coordinates the test process to test those points in parallel across a powerful virtual grid of computing resources, and (4) merges and analyzes incremental results to steer test processes in ways that improve its effectiveness and efficiency. This research has the potential to transform software development by enabling developers to formulate and apply powerful testing algorithms and by generating rich sources of data that could be analyzed and fed back to projects to drive ongoing development decisions.