Statistical Bellman-Ford algorithm with an application to retiming

Process variations in digital circuits make sequential circuit timing validation an extremely challenging task. In this paper, a Statistical Bellman-Ford (SBF) algorithm is proposed to compute the longest path length distribution for directed graphs with cycles. Our SBF algorithm efficiently computes the statistical longest path length distribution if there exist no positive cycles or detects one if the circuit is likely to have a positive cycle. An important application of SBF is Statistical Retiming based Timing Analysis (SRTA), where SBF is used to check for the feasibility of a given target clock period distribution for retiming. Our gate and wire delay distribution model considers several high-impact intra-die process parameters and accurately captures the spatial and reconvergent path correlations. The Monte Carlo simulation is used to validate the accuracy of our SBF algorithm. To the best of our knowledge, this is the first paper that propose the statistic version of the longest path algorithm for sequential circuits