Statistically Sound Verification and Optimization of Black-Box Systems

This thesis discusses two important problems for the design of practical systems under stochastic parameter variations: verification and optimization. Verification is concerned with the safety of a system, i.e., whether a system satisfies its specifications. If not, optimization is applied to tune the design parameters in the system so that the new design is safe. This thesis treats systems as black-boxes, assuming that the systems can be simulated efficiently but without detailed knowledge of the internal workings. It presents a series of simulation-based techniques to solve the problems of design verification and optimization. A notion called statistical soundness is introduced in this thesis, which guarantees that the outcome of the proposed techniques are “statistically certified” in the sense that the probability of drawing a wrong conclusion is bounded. For the problem of verification, this thesis develops a statistically sound model inference (SSMI) approach. SSMI constructs statistically sound models to explain the relationship between the stochastic parameters and the responses of a system. To improve the scalability of SSMI, a sparse approximation algorithm is also introduced. For the problem of optimization, this thesis presents a statistically sound optimization technique, SSMI-opt. SSMI-opt aims to find values of the design parameters for which the system satisfies the specifications. The proposed techniques can be applied to many interesting areas, including analog/mixd-signal circuits, embedded systems, biological systems, and medical devices. This thesis demonstrates the utility of this methodology on several interesting benchmark examples

Symbolic tolerance and sensitivity analysis of large scale electronic circuits

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