Advanced Algorithms for VLSI: Statistical Circuit Optimization and Cyclic Circuit Analysis

This work focuses on two emerging fields in VLSI. The first is use of statistical formulations to tackle one of the classical problems in VLSI design and analysis domains, namely gate sizing. The second is on analysis of nontraditional digital systems in the form of cyclic combinational circuits. In the first part, a new approach for enhancing the process-variation tolerance of digital circuits is described. We extend recent advances in statistical timing analysis into an optimization framework. Our objective is to reduce the performance variance of a technology-mapped circuit where delays across elements are represented by random variables which capture the manufacturing variations. We introduce the notion of statistical critical paths, which account for both means and variances of performance variation. An optimization engine is used to size gates with a goal of reducing the timing variance along the statistical critical paths. Circuit optimization is carried out using a gain-based gate sizing algorithm that terminates when constraints are satisfied or no further improvements can be made. We show optimization results that demonstrate an average of 72% reduction in performance variation at the expense of average 20% increase in design area. In the second part, we tackle the problem of analyzing cyclic circuits. Compiling high-level hardware languages can produce circuits containing combinational cycles that can never be sensitized. Such circuits do have well-defined functional behavior, but wreak havoc with most tools, which assume acyclic combinational logic. As such, some sort of cycle-removal step is usually necessary. We present an algorithm able to quickly and exactly characterize all combinational behavior of a cyclic circuit. It used a combination of explicit and implicit methods to compute input patterns that make the circuit behave combinationally. This can be used to restructure the circuit into an acyclic equivalent, report errors, or as an optimization aid. Experiments show our algorithm runs several orders of magnitude faster than existing ones on real-life cyclic circuits, making it useful in practice