Computational Consequences of Agreement and Ambiguity in Natural Language

The computer science technique of computational complexity analysis can provide powerful insights into the algorithm-neutral analysis of information processing tasks. Here we show that a simple, theory-neutral linguistic model of syntactic agreement and ambiguity demonstrates that natural language parsing may be computationally intractable. Significantly, we show that it may be syntactic features rather than rules that can cause this difficulty. Informally, human languages and the computationally intractable Satisfiability (SAT) problem share two costly computional mechanisms: both enforce agreement among symbols across unbounded distances (Subject-Verb agreement) and both allow ambiguity (is a word a Noun or a Verb?).

A Robust Amorphous Hierarchy from Persistent Nodes

For a very large network deployed in space with only nearby nodes able to talk to each other, we want to do tasks like robust routing and data storage. One way to organize the network is via a hierarchy, but hierarchies often have a few critical nodes whose death can disrupt organization over long distances. I address this with a system of distributed aggregates called Persistent Nodes, such that spatially local failures disrupt the hierarchy in an area proportional to the diameter of the failure. I describe and analyze this system, which has been implemented in simulation.

An Analog VLSI Chip for Estimating the Focus of Expansion

For applications involving the control of moving vehicles, the recovery of relative motion between a camera and its environment is of high utility. This thesis describes the design and testing of a real-time analog VLSI chip which estimates the focus of expansion (FOE) from measured time-varying images. Our approach assumes a camera moving through a fixed world with translational velocity; the FOE is the projection of the translation vector onto the image plane. This location is the point towards which the camera is moving, and other points appear to be expanding outward from. By way of the camera imaging parameters, the location of the FOE gives the direction of 3-D translation. The algorithm we use for estimating the FOE minimizes the sum of squares of the differences at every pixel between the observed time variation of brightness and the predicted variation given the assumed position of the FOE. This minimization is not straightforward, because the relationship between the brightness derivatives depends on the unknown distance to the surface being imaged. However, image points where brightness is instantaneously constant play a critical role. Ideally, the FOE would be at the intersection of the tangents to the iso-brightness contours at these "stationary" points. In practice, brightness derivatives are hard to estimate accurately given that the image is quite noisy. Reliable results can nevertheless be obtained if the image contains many stationary points and the point is found that minimizes the sum of squares of the perpendicular distances from the tangents at the stationary points. The FOE chip calculates the gradient of this least-squares minimization sum, and the estimation is performed by closing a feedback loop around it. The chip has been implemented using an embedded CCD imager for image acquisition and a row-parallel processing scheme. A 64 x 64 version was fabricated in a 2um CCD/ BiCMOS process through MOSIS with a design goal of 200 mW of on-chip power, a top frame rate of 1000 frames/second, and a basic accuracy of 5%. A complete experimental system which estimates the FOE in real time using real motion and image scenes is demonstrated.