Approximate property checking of mixed-signal circuits

Abstract

Growing circuit complexity and design uncertainty has made it difficult to predict whether large circuits meet target property specifications. To address this, we conservatively approximate the failure probability estimate by defining an interval that bounds this probability. Doing so using an arbitrary sampling distribution requires a learner. Given that the learner's knowledge is imperfect, the interval must first capture its uncertainty. An ensemble of such learners can then be used to compensate for the bias. Lastly, we develop an adaptive sampling scheme to tighten the obtained interval with increased simulation resources, thus controlling the accuracy vs. turn-around-time trade-off.

Leveraging pre-silicon data to diagnose out-of-specification failures in mixed-signal circuits

“…The ranking step must be rerun once we are done aggregating. The proposed approach has been demonstrated on data sampled adaptively as in [8] in Fig. 7 as well.…”

“…7(a) were built using adaptively sampled data. While a detailed discussion is outside the scope of this work, [8] first builds a failure model to predict P (F |x) using arbitrarily sampled data. P (F ) is then obtained via standard Monte Carlo estimation of this failure model.…”

“…Thus, importance sampling and adaptive sampling schemes [7,8] where the sampling distribution focuses on the failure regions are often used in practice. Obtaining the final failure estimate P (F ) from observations n…”

“…For most adaptive sampling schemes, q(x) is either highest in the failure region [7] or at the failure boundaries [8]. Thus, data sampled using q(x) can be directly used to identify failure regions.…”

“…In fact, equation (1) holds irrespective of how the circuit was sampled as long as sufficient coverage of the failure regions can be guaranteed. We use either (a) standard Monte Carlo [6] data or (b) data sampled adaptively as in [8] for the rest of this paper.…”