Synthesis of reversible circuits for testing with universal test set and C-testability of reversible iterative logic arrays

Reversibility is of interest in the design of very low-power circuits; it is essential for quantum computation. This paper examines the testability of an important subclass of reversible logic circuits that are composed of k-wire controlled NOT (k-CNOT) gates. Most commonly used stuck-at fault model (both single stuck-at fault (i.e. SSF) and multiple stuck-at fault (i.e. MSF)) has been assumed to be type of fault for such circuits. We define a universal test set (UTS) for a family C(n) of n-input circuits with respect to fault model F as a family of test sets T_UTS such that each C(n) has a unique test set T(n) in T_UTS that detects all F-type faults in every member of C(n). We show that if k ≥ 2 for all gates, then the n-wire reversible circuits have a UTS of size n with respect to MSFs. By synthesizing 0-CNOT (inverters) and 1-CNOT gates from 2-CNOT (Toffoli) gates this result can be extended to all circuits of interest. We also present a method for modifying an n-wire reversible circuit to reduce its UTS size to 3. By modeling a k-CNOT gate as a k-input AND gate and a 2-input EXOR gate we then examine testability for the SSF model. Noting their resemblance to classical (irreversible) Reed-Muller circuits, which are well known to be easily testable, we prove that the n-wire reversible circuits have a UTS of size n² + 2n + 2. Finally, we turn to the reversible counterparts of another easily-testable classical circuit family, iterative logic arrays (ILAs). We define d-dimensional reversible ILAs (RILAs) and prove that they require a constant number test vectors irrespective of array length under the single cell fault (i.e. SCF) model; this number is determined by the size of the RILA cell´s state table.