A parallel test generation for combinational circuits based on Boolean satisfiability

This paper presents an efficient parallel algebraic algorithm to implement ATPG for combinational circuits using the Boolean satisfiability on a distributed computing environment. The Path-Oriented Expanded Implication Graph (POEIG) of a combinational circuit is taken as a heuristic guide to improve the traditional stochastic calculation of the Boolean satisfiability formula of a circuit. We propose a efficient method to establish the simple reduction from complex ternary clauses to binary ones in a circuit. Based on the POEIG, a circuit is partitioned into cones according to fanout-reconvergent pairs in the circuit. To improve the performance of traditional parallel algorithms, we consider two different parallel strategies: the first for a local cone generated by our segmentation scheme, the second for a global circuit, according to the POEIG of a circuit. We introduce two important concepts for implementing our ATPG, correlative subset for a cone and precedent critical path rule within a cone in a circuit so that we can sensitize any common subpaths or cones only once. We parallel process the subcomputings of different cones based on the parallel essence of POEIG based on a decomposition algorithm.