Accurate QBF-based Test Pattern Generation in Presence of Unknown Values

Unknown (X) values may emerge during the design process as well as during system operation and test application. Sources of X-values are for example black boxes, clock-domain boundaries, analog-to-digital converters, or uncontrolled or uninitialized sequential elements. To compute a detecting pattern for a given stuck-at fault, well defined logic values are required both for fault activation as well as for fault effect propagation to observing outputs. In presence of X-values, classical test generation algorithms, based on topological algorithms or formal Boolean satisfiability (SAT) or BDD-based reasoning, may fail to generate testing patterns or to prove faults untestable. This work proposes the first efficient stuck-at fault ATPG algorithm able to prove testability or untestability of faults in presence of X-values. It overcomes the principal inaccuracy and pessimism of classical algorithms when X-values are considered. This accuracy is achieved by mapping the test generation problem to an instance of quantified Boolean formula (QBF) satisfiability. The resulting fault coverage improvement is shown by experimental results on ISCAS benchmark and larger industrial circuits.