Coherent Behavior from Incoherent Knowledge Sources in the Automatic Synthesis of Numerical Computer Programs

A fundamental problem in artificial intelligence is obtaining coherent behavior in rule-based problem solving systems. A good quantitative measure of coherence is time behavior; a system that never, in retrospect, applied a rule needlessly is certainly coherent; a system suffering from combinatorial blowup is certainly behaving incoherently. This report describes a rule-based problem solving system for automatically writing and improving numerical computer programs from specifications. The specifications are in terms of "constraints" among inputs and outputs. The system has solved program synthesis problems involving systems of equations, determining that methods of successive approximation converge, transforming recursion to iteration, and manipulating power series (using differing organizations, control structures, and argument-passing techniques).

Reflectance Map Techniques for Analyzing Surface Defects in Metal Castings

This report explores the relation between image intensity and object shape. It is shown that image intensity is related to surface orientation and that a variation in image intensity is related to surface curvature. Computational methods are developed which use the measured intensity variation across surfaces of smooth objects to determine surface orientation. In general, surface orientation is not determined locally by the intensity value recorded at each image point. Tools are needed to explore the problem of determining surface orientation from image intensity. The notion of gradient space , popularized by Huffman and Mackworth, is used to represent surface orientation. The notion of a reflectance map, originated by Horn, is used to represent the relation between surface orientation image intensity. The image Hessian is defined and used to represent surface curvature. Properties of surface curvature are expressed as constraints on possible surface orientations corresponding to a given image point. Methods are presented which embed assumptions about surface curvature in algorithms for determining surface orientation from the intensities recorded in a single view. If additional images of the same object are obtained by varying the direction of incident illumination, then surface orientation is determined locally by the intensity values recorded at each image point. This fact is exploited in a new technique called photometric stereo. The visual inspection of surface defects in metal castings is considered. Two casting applications are discussed. The first is the precision investment casting of turbine blades and vanes for aircraft jet engines. In this application, grain size is an important process variable. The existing industry standard for estimating the average grain size of metals is implemented and demonstrated on a sample turbine vane. Grain size can be computed form the measurements obtained in an image, once the foreshortening effects of surface curvature are accounted for. The second is the green sand mold casting of shuttle eyes for textile looms. Here, physical constraints inherent to the casting process translate into these constraints, it is necessary to interpret features of intensity as features of object shape. Both applications demonstrate that successful visual inspection requires the ability to interpret observed changes in intensity in the context of surface topography. The theoretical tools developed in this report provide a framework for this interpretation.

A Hierarchical Cache Coherent Protocol

As the number of processors in distributed-memory multiprocessors grows, efficiently supporting a shared-memory programming model becomes difficult. We have designed the Protocol for Hierarchical Directories (PHD) to allow shared-memory support for systems containing massive numbers of processors. PHD eliminates bandwidth problems by using a scalable network, decreases hot-spots by not relying on a single point to distribute blocks, and uses a scalable amount of space for its directories. PHD provides a shared-memory model by synthesizing a global shared memory from the local memories of processors. PHD supports sequentially consistent read, write, and test- and-set operations. This thesis also introduces a method of describing locality for hierarchical protocols and employs this method in the derivation of an abstract model of the protocol behavior. An embedded model, based on the work of Johnson[ISCA19], describes the protocol behavior when mapped to a k-ary n-cube. The thesis uses these two models to study the average height in the hierarchy that operations reach, the longest path messages travel, the number of messages that operations generate, the inter-transaction issue time, and the protocol overhead for different locality parameters, degrees of multithreading, and machine sizes. We determine that multithreading is only useful for approximately two to four threads; any additional interleaving does not decrease the overall latency. For small machines and high locality applications, this limitation is due mainly to the length of the running threads. For large machines with medium to low locality, this limitation is due mainly to the protocol overhead being too large. Our study using the embedded model shows that in situations where the run length between references to shared memory is at least an order of magnitude longer than the time to process a single state transition in the protocol, applications exhibit good performance. If separate controllers for processing protocol requests are included, the protocol scales to 32k processor machines as long as the application exhibits hierarchical locality: at least 22% of the global references must be able to be satisfied locally; at most 35% of the global references are allowed to reach the top level of the hierarchy.