Abstract-Many CAD for VLSI techniques use time-frame expansion, also known as the Iterative Logic Array representation, to model the sequential behavior of a system. Replicating industrialsize designs for many time-frames may impose impractically excessive memory requirements. This work proposes a performancedriven, succinct and parametrizable Quantified Boolean Formula (QBF) satisfiability encoding and its hardware implementation for modeling sequential circuit behavior. This encoding is then applied to three notable CAD problems, namely Bounded Model Checking (BMC), sequential test generation and design debugging. Extensive experiments on industrial circuits confirm outstanding run-time and memory gains compared to state-of-the-art techniques, promoting the use of QBF in CAD for VLSI.

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Design debugging has become a resource-intensive bottleneck in modern VLSI CAD flows, consuming as much as 60% of the total verification effort. With typical design sizes exceeding the half-million synthesized gates mark, the growing number of blocks to be examined dramatically slows down the debugging process. The aim of this work is to prune the number of debugging iterations for finding all potential bugs, without affecting the debugging resolution. This is achieved by using structural dominance relationships between circuit components. More specifically, an iterative fixpoint algorithm is presented for finding dominance relationships between multiple-output blocks of the design. These relationships are then leveraged for the early discovery of potential bugs, along with their corrections, resulting in significant debugging speed-ups. Extensive experiments on real industrial designs show that 66% of solutions are discovered early due to dominator implications. This results in consistent performance gains in all cases and a 1.7x overall speed-up for finding all potential bugs, demonstrating the robustness and practicality of the proposed approach.

With lower supply voltages, increased integration densities and higher operating frequencies, power grid verification has become a crucial step in the VLSI design cycle. The accurate estimation of maximum instantaneous power dissipation aims at finding the worst-case scenario where excessive simultaneous switching could impose extreme current demands on the power grid. This problem is highly input-pattern dependent and is proven to be NP-hard. In this work, we capitalize on the compelling advancements in satisfiability solvers to propose a pseudo-Boolean satisfiability-based framework that reports the input patterns maximizing circuit activity, and consequently peak dynamic power, in combinational and sequential circuits. The proposed framework is enhanced to handle unit gate delays and output glitches. In order to disallow unrealistic input transitions, we show how to integrate input constraints in the formulation. Finally, a number of optimization techniques, such as the use of gate switching equivalence classes, are described to improve the scalability of the proposed method. An extensive suite of experiments on ISCAS85 and ISCAS89 circuits confirms the robustness of the approach compared to simulation-based techniques and encourages further research for low-power solutions using Boolean satisfiability.

Abstract-With the growing complexity of VLSI designs, functional debugging has become a bottleneck in modern CAD flows. To alleviate this cost, various SAT-based techniques have been developed to automate bug localization in the RTL. In this context, dominance relationships between circuit blocks have been recently shown to reduce the number of SAT solver calls, using the concept of solution implications. This paper first introduces the dual concepts of reverse domination and non-solution implications. A SAT solver is tailored to leverage reverse dominators for the early on-the-fly detection of bug-free components. These are nonsolution areas and their early pruning significantly reduces the the debugging search-space. This process is expedited by branching on error-select variables first. Extensive experiments on tough real-life industrial debugging cases show an average speedup of 1.7x in SAT solving time over the state-of-the-art, a testimony of the practicality and effectiveness of the proposed approach.