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A complete function-based scheme is presented to identify at-speed sequentially untestable path delay faults. We introduce signature variables to implicitly track error propagation through combinational and sequential circuits. The path sensitization test functions are encoded with the signature variables. These encoded test functions allow implicit identification of all propagating transitions corresponding to each individual test function minterm. We then utilize the signature variables during the fault propagation in a way such that the latched error propagates robustly to an observable point irrespective of other latched errors. Results presented on the ISCAS'89 benchmarks show a large number of sequentially untestable path delay faults are identified.