As-Robust-As-Possible test generation in the presence of small delay defects using pseudo-Boolean optimization

Delay testing is performed to guarantee that a manufactured chip is free of delay defects and meets its performance specification. However, only few delay faults are robustly testable. For robustly untestable faults, non-robust tests which are of lesser quality are typically generated. Due to significantly relaxed conditions, there is a large quality gap between non-robust and robust tests. This paper presents a test generation procedure for As-Robust-As-Possible (ARAP) tests to increase the overall quality of the test set. Instead of generating a non-robust test for a robustly untestable fault, an ARAP test is generated which maximizes the number of satisfiable conditions required for robust test generation by pseudo-Boolean optimization. Additionally, the problem formulation is extended to incorporate the increased significance of small delay defects. By this, the likeliness that small delay defects invalidate the test is reduced. Experimental results on large industrial circuits confirm the quality gap and show that the generated ARAP tests satisfy a large percentage of all robustness conditions on average which signifies a very high quality.