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We present a generic framework that supports efficient generation of the traditional Boolean difference function of some output with respect to any line in a combinational circuit, which is important when testing for logic defects. The framework also allows for the generation of generalized Boolean difference functions, which reflect sensitivity on event propagation from a given line to some circuit output. This generalized function could apply in timing verification, analysis, and test. We implemented the proposed framework using various function representation environments, including binary decision diagrams, Boolean expression diagrams, and Boolean networks, and report experimental results on the ISCAS'85 and ISCAS'89 benchmarks.