Full-chip verification methods for DSM power distribution systems
DAC '98 Proceedings of the 35th annual Design Automation Conference
Analog circuit sizing based on formal methods using affine arithmetic
Proceedings of the 2002 IEEE/ACM international conference on Computer-aided design
Proceedings of the 40th annual Design Automation Conference
First-order incremental block-based statistical timing analysis
Proceedings of the 41st annual Design Automation Conference
Fast statistical timing analysis handling arbitrary delay correlations
Proceedings of the 41st annual Design Automation Conference
Fast interval-valued statistical interconnect modeling and reduction
Proceedings of the 2005 international symposium on Physical design
An efficient algorithm for statistical minimization of total power under timing yield constraints
Proceedings of the 42nd annual Design Automation Conference
Probabilistic interval-valued computation: representing and reasoning about uncertainty in dsp and vlsi design
Asymptotic probability extraction for non-normal distributions of circuit performance
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Interval-valued reduced order statistical interconnect modeling
Proceedings of the 2004 IEEE/ACM International conference on Computer-aided design
Timing budgeting under arbitrary process variations
Proceedings of the 2007 IEEE/ACM international conference on Computer-aided design
Distribution arithmetic for stochastical analysis
Proceedings of the 2008 Asia and South Pacific Design Automation Conference
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Interval methods offer a general, fine-grain strategy for modeling correlated range uncertainties in numerical algorithms. We present a new, improved interval algebra that extends the classical affine form to a more rigorous statistical foundation. Range uncertainties now take the form of confidence intervals. In place of pessimistic interval bounds, we minimize the probability of numerical "escape"; this can tighten interval bounds by 10X, while yielding 10-100X speedups over Monte Carlo. The formulation relies on three critical ideas: liberating the affine model from the assumption of symmetric intervals; a unifying optimization formulation; and a concrete probabilistic model. We refer to these as probabilistic intervals, for brevity. Our goal is to understand where we might use these as a surrogate for expensive, explicit statistical computations. Results from sparse matrices and graph delay algorithms demonstrate the utility of the approach, and the remaining challenges.