Features of Machine Learning and Other Topics in Foundations of Computing

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This project will contribute toward the goal of understanding how a computer can be programmed to learn by isolating features of incremental learning algorithms that theoretically enhance their learning potential. The features are chosen to resemble features of human learning. For example, learning devices that use the results of one learning episode to aid in the next learning endeavor will be considered. Another powerful learning technique, for both humans and machines, is the ability to ask questions. Investigations into the relative learning potential of algorithms as the language they use to pose questions will be conducted. Preliminary results indicate that the more powerful the query language used, the greater the learning potential of the device asking questions. Parameters of query language strength such as the number of quantifiers and the number of alternations of quantifiers will be vigorously examined. Current program testing techniques do not and cannot determine correctness precisely. The purpose of these techniques is to reveal errors in a program; however, if no errors are found, no measure is given as to how reliable the program is. Therefore there is no notion of how "close" to correct the tested program is. The goal of this research is to develop a theory whereby it is possible to say precisely how reliable a program is when it passes a given test.