This paper introduces τk notation to be used to assess test generation complexity of classes of sequential circuits. Using τk notation, we reconsider and restate the time complexity of test generation for existing classes of acyclic sequential circuits. We also introduce a new DFT method called feedback shift register (FSR) scan design technique, which is extended from the scan design technique. Therefore, for a given sequential circuit, the corresponding FSR scan designed circuit has always equal or lower area overhead and test application time than the corresponding scan designed circuit. Furthermore, we identify some new classes of sequential circuits that contain some cyclic sequential circuits, which are τ-equivalent and τ2-bounded. These classes are the l-length-bounded testable circuits, l-length-bounded validity-identifiable circuits, t-time-bounded testable circuits and t-time-bounded validity-identifiable circuits. In addition, we provide two examples of circuits belonging to these classes, namely counter-cycle finite state machine realizations and state-shiftable finite state machine realizations. Instead of using a DFT method, a given sequential circuit described at the finite state machine (FSM) level can be synthesized using another test methodology called synthesis for testability (SFT) into a circuit that belongs to one of the easily testable classes of cyclic sequential circuits.

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 provide a practical formulation of the problem of identifying all error occurrences and all failed scan cells in at-speed scan based BIST environment. We propose a method that can be used to identify every error when the circuit test frequency is higher than the tester frequency. Our approach requires very little extra hardware for diagnosis and the test application time required to identify errors is a linear function of the frequency ratio between the CUT and the tester.