A probably approximately correct framework to estimate performance degradation in embedded systems

Future design environments for embedded systems will require the development of sophisticated computer-aided design tools for compiling the high-level specifications of an application down to a final low-level language describing the embedded solution. This requires abstraction of technology-dependent aspects and requirements into behavioral entities. The paper takes a first step in this direction by introducing a high-level methodology for estimating the performance degradation of an application affected by perturbations; a special emphasis is given to accuracy performance. To grant generality it is uniquely assumed that the performance degradation function and the mathematical formulation describing the application are Lebesgue measurable. Perturbations affecting the application abstract details related to physical sources of uncertainties such as finite precision representation, faults, fluctuations of physical parameters, battery power variations, and aging effects whose impact on the computation can be treated within a high-level homogenous framework. A novel stochastic theory based on randomization is suggested to quantify the approximated nature of the perturbed environment. The outcomes are two algorithms which estimate in polynomial time the performance degradation of the application once affected by perturbations. Such information can then be exploited by HW/SW codesign methodologies to guide the subsequent partitioning between HW and SW, analog versus digital, fixed versus floating point, or used to validate architectural choices before any low-level design step takes place. The proposed method is finally applied to real designs involving neural and wavelet-based applications.