Constrained random simulation is the main workhorse in today’s hardware verification flows. It requires the random generation of input stimuli that obey a set of declaratively specified input constraints, which are then applied to validate given design properties by simulation. The efficiency of the overall flow depends critically on (1) the performance of the constraint solver and (2) the distribution of the generated solutions. In this paper we discuss the overall problem of efficient constraint solving for stimulus generation for mixed Boolean/integer variable domains and propose a new hybrid solver based on Markov-chain Monte Carlo methods with good performance and distribution. 1

Despite the increasing research effort in formal verification, constraintbased random simulation remains an integral part of design validation, especially for large design components where formal techniques do not scale. However, effective simulation often requires the construction of complex constraints to stimulate important aspects of the design. In this paper we present Toggle, a novel solution which automatically identifies those regions of the design which are not sufficiently exercised in random simulation. Toggle then generates legal random stimulus of the primary inputs of the design to improve coverage over those regions, by augmenting the toggling activity of the signals internal to the region. In addition, Toggle can also be used to toggle a set of user-specified signals anywhere in the design. Experimental results indicate that Toggle can stimulate regions of a design in much fewer simulation cycles than random simulation, leading to simulation runs which can potentially expose bugs sooner. 1.

We introduce novel algorithms for generating random solutions from a uniform distribution over the solutions of a boolean satisfiability problem. Our algorithms operate in two phases. In the first phase, we use a recently introduced SampleSearch scheme to generate biased samples while in the second phase we correct the bias by using either Sampling/Importance Resampling or the Metropolis-Hastings method. Unlike state-of-the-art algorithms, our algorithms guarantee convergence in the limit. Our empirical results demonstrate the superior performance of our new algorithms over several competing schemes.

for inspiring me to consider various fields of research and providing feedback on my projects and papers. I also want to thank my defense committee for their comments and insights: Professor John Hayes, Professor Karem Sakallah, and Professor Dennis Sylvester. I would like to thank Professor David Kieras for enhancing my knowledge and appreciation for computer programming and providing invaluable advice. Over the years, I have been fortunate to know and work with several wonderful students. I have collaborated extensively with Kai-hui Chang and Smita Krishnaswamy and have enjoyed numerous research discussions with them and have benefited from their insights. I would like to thank Ian Kountanis and Zaher Andraus for our many fun discussions on parallel SAT. I also appreciate the time spent collaborating with Kypros Constantinides and Jason Blome. Although I have not formally collaborated with Ilya Wagner, I have enjoyed numerous discussions with him during my doctoral studies. I also thank my office mates Jarrod Roy, Jin Hu, and Hector Garcia. Without my family and friends I would never have come this far. I would like to thank Geoff Blake and Smita Krishnaswamy, who have been both good friends and colleagues

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suite of secure multi-party computation algorithms for solving

Up to now we focused almost exclusively on exact algorithms for processing graphical models and we emphasized the two styles of inference (exemplified by variable elimination schemes) and search, or conditioning, exemplified by AND/OR search or backtracking search (for constraint networks). We also showed that hybrids of search and inference are effective and can be used to trade space for time. Clearly, due to the hardness of the tasks we address, some networks cannot be processed exactly because their structure is not sparse enough; its treewidth is too high, and the functions themselves do not posses any property that can be exploited. In such cases approximation algorithms are the only choice. Approximation algorithms can also be designed as either approximating an inference scheme, or as approximating search. Bounded inference algorithms, on which this chapter focuses, approximate inference, while sampling scheme can be viewed as approximating search. This chapter presents a class of approximation algorithms that bound the dimensionality of dependencies created by inference algorithms. This yields a collection of parameterized schemes of mini-buckets, mini-clustering and iterative join-graph propagation that offers adjustable trade-off between accuracy and efficiency. It was shown that approximation scheme within given relative error bounds is NPhard [57, 67]. Nevertheless there are approximation strategies that work well in practice. One alternative for dealing with these bleak fact is to develop anytime algorithms. These algorithms can be interrupted at any time producing the best solution found thus far. Other methodology is to exploit the special structure of the problem or to aim at providing 175>-

Itiswellknownthatcomputingrelativeapproximationsofweightedcountingqueries such as the probability of evidence in a Bayesian network, the partition function of a Markov network, and the number of solutions of a constraint satisfaction problem is NP-hard. In this paper, we settle therefore on an easier problem of computing highconfidence lower bounds and propose an algorithm based on importance sampling and Markov inequality for it. However, a straight-forward application of Markov inequality often yields poor lower bounds because it uses only one sample. We therefore propose several new schemes that extend it to multiple samples. Empirically, we show that our new schemes are quite powerful, often yielding substantially higher (better) lower bounds than state-of-the-art schemes. 1

Abstract not found