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 τ k-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.