The complex aerospace systems of the future will challenge the capabilities of present-day software engineering, which is reaching cost and complexity limits of development technologies evolved in the first fifty years of computing. A new science for the next fifty years is required to transform software engineering into a computational discipline capable of fast and dependable software development. This paper describes verification and certification challenges for avionics software, in particular, the need to verify behavior in all circumstances of use. The emerging technology of function extraction (FX) for automated computation of software behavior is discussed as a new technology for avionics software certification. An FX demonstration system is employed to illustrate the role of behavior computation in the avionics certification process.