ATPG Using Fast Justification and Propagation on the Implication Graph

Automatic Test Pattern Generation (ATPG) primarily has to solve three fundamental Boolean problems: justification, propagation, and implication. In the past, various data structures (e.g. netlists, CNFs, decision diagrams) have been used to tackle these problems with none of them being specifically optimized for all these tasks. That is why we propose fast and optimized algorithms for justification, propagation, and implication that are part of a versatile and efficient SAT based implication engine [1]. It inherits the advantages of structural as well as SAT based techniques as it includes all topological and functional information into a single graph model of the CNF, called implication graph (IG) [1]. The multitude of heuristics developed for structural techniques can directly be transfered to the IG. As the complex functional operations of justification, propagation, and implication reduce to simple graph algorithms they are easily extended to make use of bitparallel techniques resulting in a high efficiency. This paper introduces new methods for fast IG based justification and propagation that are included into the implication engine of [1]. Using these algorithms our tool TIP outperforms the state-of-the-art in structural and SAT based ATPG. Since the IG is automatically generated for an arbitrary logic and the presented algorithms for justification and implication remain applicable independent of the chosen logic, ATPG for various fault models can easily be built on top of the same engine. Tools for pathdelay, gate delay, and stuck-at fault models have already been developed.