We present an analysis to automatically determine if a program represents a continuous function, or equivalently, if infinitesimal changes to its inputs can only cause infinitesimal changes to its outputs. The analysis can be used to verify the robustness of programs whose inputs can have small amounts of error and uncertainty---e.g., embedded controllers processing slightly unreliable sensor data, or handheld devices using slightly stale satellite data.
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Chaudhuri et al. (2010) studied this question.
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