Formal equivalence verifiers for combinational circuits rely heavily on BDD algorithms. However, building monolithic BDDs is often not feasible for today's complex circuits. Thus, to increase the effectiveness of BDD-based comparisons, divide-and-conquer strategies based on cut-points are applied. Unfortunately, these algorithms may produce false negatives. Significant effort must then be spent for determining whether the failures are indeed real. In particular, if the design is actually incorrect, many cut-point based algorithms perform very poorly. In this paper we present a new algorithm that completely removes the problem of false negatives by introducing normalized functions instead of free variables at cut points. In addition, this approach handles the propagation of input assumptions to cut-points, is significantly more accurate in finding cut-points, and leads to more efficient counter-example generation for incorrect circuits. Although, naively, our algorithm 1 would appear to be more expensive than traditional cut-point techniques, the empirical data on more than 900 complex signals from a recent microprocessor design, shows rather the opposite.

The developments of efficient SAT solvers have attracted tremendous research interest in recent years. The merits of these solvers are often compared in terms of their performance based upon a wide spread of benchmarks. In this paper, we extend an earlier-proposed solver design concept called (SCGL) Signal Correlation Guided Learning that is ATPG-based into a family of heuristics. Along with this SCGL family of heuristics, we classify benchmark examples according to their performance using the SCGL heuristics. With this study, we identify the class of problems that are uniquely suitable to be solved by using the SCGL approach. In particular, for solving difficult circuit-based problems at INTEL, our SCGL-based ATPG solver is able to achieve at least an order of magnitude speedup over the state-of-the-art SAT solvers. Our conclusion is that SCGL is an unique solver design concept that can complement heuristics proposed by others for solving circuit-oriented difficult problems.

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Commonly used pattern sources in simulation-based verification include random, guided random, or design verification patterns. Although these patterns may help bring the design to those hard-to-reach states for activating the errors and for propagating them to observation points, they tend to be very long, which complicates the subsequent diagnosis process. As a key step in reducing the overall diagnosis complexity, we propose a method of generating a shorter error-sequence based on a given long error-sequence. We formulate the problem as a satisfiability problem and employ a SAT solver as the underlying engine for this task. By heuristically selecting an intermediate state S i which is reachable by the given long sequence, the task of finding the transfer sequence from the initial state to the target state can be divided into two easier tasks -finding a transfer sequence from the initial state to S i and one from S i to the target state. Our preliminary experimental results on public benchmark circuits show that the proposed method can achieve significant reduction in the length of the error sequences.