Abstract — In today’s SoC design cycles, debugging is one of the most time consuming manual tasks. CAD solutions strive to reduce the inefficiency of debugging by identifying error sources in designs automatically. Unfortunately, the capacity and performance of such automated techniques must be considerably extended for industrial applicability. This work aims to improve the performance of current state-of-the-art debugging techniques, thus making them more practical. More specifically, this work proposes a novel design debugging formulation based on maximum satisfiability (max-sat) and approximate max-sat. The developed technique can quickly discard many potential error sources in designs, thus drastically reducing the size of the problem passed to an existing debugger. The max-sat formulation is used as a pre-processing step to construct a highly optimized debugging framework. Empirical results demonstrate the effectiveness of the proposed framework as run-time improvements of orders of magnitude are consistently realized over a state-ofthe-art debugger. I.

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. I.

Abstract—With lower supply voltages, increased integration densities and higher operating frequencies, power grid verification has become a crucial step in the very large-scale integration 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 inputpattern dependent and is proven to be NP-hard. In this paper, we capitalize on the compelling advancements in satisfiability (SAT) solvers to propose a pseudo-Boolean SAT-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 SAT. Index Terms—Maximum circuit activity, peak dynamic power, pseudo-Boolean satisfiability, SAT. I.

Design debugging is one of the major remaining manual processes in the semiconductor design cycle. Despite recent advances in the area of automated design debugging, more effort is required to cope with the size and complexity of today’s designs. This paper introduces an abstraction and refinement methodology to enable current debuggers to operate on designs that are orders of magnitude larger than otherwise possible. Two abstraction techniques are developed with the goals of improving debugger performance for different circuit structures: State abstraction is aimed at reducing the problem size for circuits consisting purely of primitive gates, while function abstraction focuses on designs that also contain modular and hierarchical information. In both methods, after an initial abstracted model is created, the problem can be solved by an existing automated debugger. If an error site is abstracted, refinement is necessary to reintroduce some of the abstracted components back into the design. This paper also presents the underlying theory to guarantee correctness and completeness of a debugging tool that operates using the proposed methodology. Empirical results demonstrate improvements in run time and memory capacity of two orders of magnitude over a state-of-the-art debugger on a wide range of benchmark and industrial designs.

Abstract—Design debugging is becoming an increasingly difficult task in the VLSI design flow with the growing size of modern designs and their error traces. In this work, a novel abstraction and refinement technique for design debugging is presented that addresses two key components of the debugging complexity, the design size and the error trace length. The abstraction technique works by under-approximating the debugging problem by removing modules of the original design and replacing them problem is solved, the refinement strategy uses the resulting UNSAT core to direct which modules should be refined. This refinement strategy is extended by allowing refinement of across time-frames in addition to modules. Experimental results show that the proposed algorithm is able to return solutions for all instances compared to only 41 % without the technique demonstrating the viability of this approach in tackling realworld debugging problems. I.

Design debugging is a major bottleneck in modern VLSI design flows as both the design size and the length of the error trace contribute to its inherent complexity. With typical design blocks exceeding half a million synthesized logic gates and error traces in the thousands of clock cycles, the complexity of the debugging problem poses a great challenge to automated debugging techniques. This work aims to address this daunting challenge by introducing the Bounded Model Debugging methodology that iteratively analyzes bounded sequences of the error trace. Two techniques are introduced in this methodology to solve this growing problem. The first technique iteratively analyzes bounded subsequences of the error trace of increasing size until the error is found or the entire trace is analyzed. The second technique partitions the error trace into non-overlapping bounded sequences of clock cycles which are each separately analyzed. A discussion of these two techniques is presented and a unified methodology that leverages the strengths of both techniques is developed. Empirical results on real industrial designs show that for large designs and long error traces the proposed methodology can find the actual error in 79 % of cases with the first technique and 100 % of cases with the second technique. In cases where the methodology is not used only 21% of cases are able to find the actual error. These numbers confirm the benefits of the proposed methodology to allow conventional automated debuggers to handle much larger real-life circuits.

Abstract—Given an erroneous design, functional verification returns an error trace exhibiting a mismatch between the specification and the implementation of a design. Automated design debugging uses these error traces to identify potentially erroneous modules causing the error. With the increasing size and complexity of modern VLSI designs, error traces have become longer and harder to analyze. At the same time, design debugging has become one of the most resource-intensive steps in the chip design cycle. This work proposes a scalable SATbased design debugging algorithm that uses interpolants to over-approximate sets of constraints that model the erroneous behavior. The algorithm partitions the original problem into a sequence of smaller subproblems by using subsections of the error trace that are examined iteratively. This is made possible by using interpolants to properly constrain the erroneous behavior for each subproblem, significantly reducing the number of simultaneous time-frames examined in the error trace. The described method is shown to be complete and an additional technique is presented to improve the quality of the debugging results using multiple interpolants. Experiments on real designs show a 57 % reduction in memory and 23 % decrease in run-time compared to previous work. I.

Managing long verification error traces is one of the key challenges of automated debugging engines. Today, debuggers rely on the iterative logic array to model sequential behavior which drastically limits their application. This work presents Bounded Model Debugging, an iterative, systematic and practical methodology to allow debuggers to tackle larger problems than previously possible. Based on the empirical observation that errors are excited in temporal proximity of the observed failures, we present a framework that improves performance by up to two orders of magnitude and solve 2.7 × more problems than a conventional debugger.

As contemporary VLSI designs grow in complexity, design debugging has rapidly established itself as one of the largest bottlenecks in the design cycle today. Automated debug solutions such as those based on Boolean Satisfiability (SAT) enable engineers to reduce the debug effort by localizing possible error sources in the design. Unfortunately, adaptation of these techniques to industrial designs is still limited by the performance and capacity of the underlying engines. This paper presents a novel formulation of the debugging problem using MaxSat to improve the performance and applicability of automated debuggers. Our technique not only identifies errors in the design but also indicates when the bug is excited in the error trace. MaxSat allows for a simpler formulation of the debugging problem, reducing the problem size by 80 % compared to a conventional SATbased technique. Empirical results demonstrate the effectiveness of the proposed formulation as run-time improvements of 4.5× are observed on average. This work introduces two performance improvements to further reduce the time required to find all error sources within the design by an order of magnitude.

Abstract—Computer-aided design tools are continuously improving their scalability and efficiency to mitigate the high cost associated with designing and fabricating modern VLSI systems. A key step in the design process is the root-cause analysis of detected errors. Debugging may take months to close, introduce high cost and uncertainty ultimately jeopardizing the chip release date. This study makes the case for debug automation in each part of the design flow (RTL to silicon) to bridge the gap. Contemporary research, challenges and future directions motivate for the urgent need in automation to relieve the pain from this highly manual task. I.