Testability of Reversible Iterative Logic Arrays

TL;DR

This paper investigates the testability of reversible iterative logic arrays, demonstrating their constant-testability and optimal-testability, and presents efficient test generation algorithms applicable to various dimensions.

Contribution

It introduces the concepts of C-Testability, O-Testability, and U-Testability for reversible ILAs and provides cycle-based algorithms for efficient test generation.

Findings

Reversible ILAs are proven to be C-Testable and O-Testable.

Test set size remains constant for certain ILAs regardless of size.

Efficient test generation algorithms are developed for 1-D and 2-D ILAs.

Abstract

Iterative Logic Arrays (ILAs) are ideal as VLSI sub-systems because of their regular structure and its close resemblance with FPGAs (Field Programmable Gate Arrays). Reversible circuits are of interest in the design of very low power circuits where energy loss implied by high frequency switching is not of much consideration. Reversibility is essential for Quantum Computing. This paper examines the testability of Reversible Iterative Logic Arrays (ILAs) composed of reversible k-CNOT gates. For certain ILAs it is possible to find a test set whose size remains constant irrespective of the size of the ILA, while for others it varies with array size. Former type of ILAs is known as Constant-Testable, i.e. C-Testable. It has been shown that Reversible Logic Arrays are C-Testable and size of test set is equal to number of entries in cells truth table implying that the reversible ILAs are also Optimal-Testable, i.e. O-Testable. Uniform-Testability, i.e. U-Testability has been defined and Reversible Heterogeneous ILAs have been characterized as U-Testable. The test generation problem has been shown to be related to certain properties of cycles in a set of graphs derived from cell truth table. By careful analysis of these cycles an efficient test generation technique that can be easily converted to an ATPG program has been presented for both 1-D and 2D ILAs. The same algorithms can be easily extended for n-Dimensional Reversible ILAs.