Due to the exponential growth of both design complexity and the number of gates per pin, functional debugging has emerged as a critical step in the development of a system-on-chip. We introduce a novel debugging approach for programmable systems-on-chip. The new method leverages the advantages of the two complementary functional execution approaches, emulation and simulation. We have developed a set of tools, transparent to both the design and debugging process, which enables the user to run long test sequences in emulation, and upon error detection, roll-back to an arbitrary instance in execution time, and switch over to simulationbased debugging for full design visibility and controllability. The efficacy of the approach is dependent on the method for transferring the computation from one execution domain to another. To enable effective transfer of the computation state, we have identified a set of optimization tasks, established their computation complexity, and developed an efficient suite of optimization algorithms.