Dimension reduction in statistical simulation of digital circuits

Statistical analysis tasks are increasingly encountered in the design of digital circuits that implement complex Boolean functions. Examples include analyzing the impact of soft errors, estimating power consumption, and stochastic computation. Common simulation techniques such as quasiMonte Carlo simulation often converge too slowly for large circuits with many inputs, i.e., many dimensions. We analyze the probabilistic properties of Boolean functions, and identify new function classes called correlation insensitive (CI) which tolerate input dependencies. Correlation insensitivity enables dimension reduction, thereby significantly improving simulation quality. We investigate the theory of CI functions, present a new dimension-reduction algorithm, and show useful links to some well-known circuit design problems. Author