In this paper, we discuss the relationship between the test generation complexity for path delay faults (PDFs) and that for stuck-at faults (SAFs) in combinational and sequential circuits using the recently introduced τk-notation. On the other hand, we also introduce a class of cyclic sequential circuits that are easily testable, namely two-column distributive state-shiftable finite state machine realizations (2CD-SSFSM). Then, we discuss the relevant conjectures and unsolved problems related to the test generation for sequential circuits with PDFs under different clock schemes and test generation models.

In this paper, we propose an alternative method that does not generate a test for each path delay fault directly to generate tests for path delay faults. The proposed method generates an N-propagation test-pair set by using an Ni-detection test set for single stuck-at faults. The N-propagation test-pair set is a set of vector pairs which contains N distinct vector pairs for every transition faults at a check point. Check points consist of primary inputs and fanout branches in a circuit. We do not target the path delay faults for test generation, instead, the N-propagation test-pair set is generated for the transition (both rising and falling) faults of check points in the circuit. After generating tests, tests are simulated to determine their effectiveness for singly testable path delay faults and robust path delay faults. Results of experiments on the ISCAS'85 benchmark circuits show that the N-propagation test-pair sets obtained by our method are effective in testing path delay faults.