Fault testing for reversible circuits

Irreversible computation necessarily results in energy dissipation due to information loss. While small in comparison to the power consumption of today's VLSI circuits, if current trends continue this will be a critical issue in the near future. Reversible circuits offer an alternative that, in principle, allows computation with arbitrarily small energy dissipation. Furthermore, reversible circuits are essential components of quantum logic. We consider the problem of testing these circuits, and in particular generating efficient test sets. The reversibility property significantly simplifies the problem, which is generally hard for the irreversible case. We discuss conditions for a test set to be complete, give a number of practical constructions, and consider test sets for worst-case circuits. In addition, we formulate the problem of finding minimal test sets into an integer linear program (ILP) with binary variables. While this ILP method is infeasible for large circuits, we show that combining it with a circuit decomposition approach yields a practical alternative.