Three Cuts for Accelerated Interval Propagation

This paper addresses the problem of nonlinear multivariate root finding. In an earlier paper we described a system called Newton which finds roots of systems of nonlinear equations using refinements of interval methods. The refinements are inspired by AI constraint propagation techniques. Newton is competative with continuation methods on most benchmarks and can handle a variety of cases that are infeasible for continuation methods. This paper presents three "cuts" which we believe capture the essential theoretical ideas behind the success of Newton. This paper describes the cuts in a concise and abstract manner which, we believe, makes the theoretical content of our work more apparent. Any implementation will need to adopt some heuristic control mechanism. Heuristic control of the cuts is only briefly discussed here.

An Accelerated Chow and Liu Algorithm: Fitting Tree Distributions to High Dimensional Sparse Data

Chow and Liu introduced an algorithm for fitting a multivariate distribution with a tree (i.e. a density model that assumes that there are only pairwise dependencies between variables) and that the graph of these dependencies is a spanning tree. The original algorithm is quadratic in the dimesion of the domain, and linear in the number of data points that define the target distribution $P$. This paper shows that for sparse, discrete data, fitting a tree distribution can be done in time and memory that is jointly subquadratic in the number of variables and the size of the data set. The new algorithm, called the acCL algorithm, takes advantage of the sparsity of the data to accelerate the computation of pairwise marginals and the sorting of the resulting mutual informations, achieving speed ups of up to 2-3 orders of magnitude in the experiments.

Test Generation Guided Design for Testability

This thesis presents a new approach to building a design for testability (DFT) system. The system takes a digital circuit description, finds out the problems in testing it, and suggests circuit modifications to correct those problems. The key contributions of the thesis research are (1) setting design for testability in the context of test generation (TG), (2) using failures during FG to focus on testability problems, and (3) relating circuit modifications directly to the failures. A natural functionality set is used to represent the maximum functionalities that a component can have. The current implementation has only primitive domain knowledge and needs other work as well. However, armed with the knowledge of TG, it has already demonstrated its ability and produced some interesting results on a simple microprocessor.