Accurate X-Propagation for Test Applications by SAT-Based Reasoning

Unknown or X-values during test applications may originate from uncontrolled sequential cells or macros, from clock or A/D boundaries, or from tristate logic. The exact identification of X-value propagation paths in logic circuits is crucial in logic simulation and fault simulation. In the first case, it enables the proper assessment of expected responses and the effective and efficient handling of X-values during test response compaction. In the second case, it is important for a proper assessment of fault coverage of a given test set and consequently influences the efficiency of test pattern generation. The commonly employed
n
-valued logic simulation evaluates the propagation of X-values only pessimistically, i.e., the X-propagation paths found by
n
-valued logic simulation are a superset of the actual propagation paths. This paper presents an efficient method for overcoming this pessimism and for determining accurately the set of signals that carry an X-value for an input pattern. As examples, it investigates the influence of this pessimism on the two applications, X-masking and stuck-at fault coverage assessment. The experimental results on benchmark and industrial circuits assess the pessimism of classic algorithms and show that these algorithms significantly overestimate the signals with X-values. The experiments show that overmasking of test data during test compression can be reduced by an accurate analysis. In stuck-at fault simulation, the coverage of the test set is increased by the proposed algorithm without incurring any overhead.