We present an effective technique for crosschecking a C or C++ program against an accelerated OpenCL version, as well as a technique for detecting data races in OpenCL programs. Our techniques are implemented in KLEE-CL, a symbolic execution engine based on KLEE and KLEE-FP that supports symbolic reasoning on the equivalence between symbolic values. Our approach is to symbolically model the Ope...

By introducing some redundant Klee-Minty constructions, we have previously shown that the central path may visit every vertex of the Klee-Minty cube having 2 − 2 “sharp” turns in dimension n. In all of the previous constructions, the maximum of the distances of the redundant constraints to the corresponding facets is an exponential number of the dimension n, and those distances are decaying geo...

By introducing redundant Klee-Minty examples, we have previously shown that the central path can be bent along the simplex path. In this paper, we seek for an analogous result for the volumetric path defined by the volumetric barrier function. Although we only have a complete proof in 2D, the evidence provided by some illustrations anticipates that a KleeMinty construction exists for the volume...

We systematically investigate the farthest distance function, farthest points, Klee sets, and Chebyshev centers, with respect to Bregman distances induced by Legendre functions. These objects are of considerable interest in Information Geometry and Machine Learning; when the Legendre function is specialized to the energy, one obtains classical notions from Approximation Theory and Convex Analys...