Smooth interpretation

We present smooth interpretation, a method for systematic approx-imation of programs by smooth mathematical functions. Programs from many application domains make frequent use of discontin-uous control flow constructs, and consequently, encode functions with highly discontinuous and irregular landscapes. Smooth in-terpretation algorithmically attenuates such irregular features. By doing so, the method facilitates the use of numerical optimization techniques in the analysis and synthesis of programs. Smooth interpretation extends to programs the notion of Gaus-sian smoothing, a popular signal-processing technique that filters out noise and discontinuities from a signal by taking its convolu-tion with a Gaussian function. In our setting, Gaussian smooth-ing executes a program P according to a probabilistic semantics. Specifically, the execution of P on an input x after smoothing is a