terminating version of middle-out reasoning for lemma speculation. This supports automatic speculation of schematic lemmas which are incrementally instantiated by unification as the rippling proof progresses. Middle-out reasoning and lemma speculation have been implemented in higher-order logic and evaluated

Abstract. Lemma speculation has long been considered a promising technique to automate the discovery of missing lemmas for inductive proofs. This technique involves speculating a schematic lemma that becomes incrementally instantiated by unification as the proof continues. This synthesis process

The principle aim of this dissertation is to investigate the philosophical application of quantum information theory to interpretational issues regarding the theory of quantum mechanics. Recently, quantum information theory has emerged as a potential source for such an interpretation. The main

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Effective support for custom proof automation is essential for large-scale interactive proof develop-ment. However, existing languages for automation via tactics either (a) provide no way to specify the behavior of tactics within the base logic of the accompanying theorem prover, or (b) rely

The origin of the spacetime metric: Bell’s ‘Lorentzian pedagogy ’ and its significance in general relativity ∗

The origin of the spacetime metric: Bell’s ‘Lorentzian pedagogy ’ and its significance in general relativity ∗

The compressive sensing (CS) framework aims to ease the burden on analog-to-digital converters (ADCs) by exploiting inherent structure in natural and man-made signals. It has been demon-strated that structured signals can be acquired with just a small number of linear measurements, on the order of the signal complexity. In practice, this enables lower sampling rates that can be more easily achieved by current hardware designs. The primary bottleneck that limits ADC sam-pling rates is quantization, i.e., higher bit-depths impose lower sampling rates. Thus, the decreased sampling rates of CS ADCs accommodate the otherwise limiting quantizer of conventional ADCs. In this thesis, we consider a different approach to CS ADC by shifting towards lower quantizer bit-depths rather than lower sampling rates. We explore the extreme case where each measurement is quantized to just one bit, representing its sign. We develop a new theoretical framework to analyze this extreme case and develop new algorithms for signal reconstruction from such coarsely quantized measurements. The 1-bit CS framework leads us to scenarios where it may be more appropriate to reduce bit-depth instead of sampling rate. We find that there exist two distinct regimes of operation that correspond to high/low signal-to-noise ratio (SNR). In the measurement

First, I would like to thank to Dimka Karastoyanova and Mariano Cilia for all the fruitful discussions, their guidance and support through the course of this project. Thanks also to Prof. Alejandro Buchmann who sponsored my stay at Technische Universität Darmstadt during the spring of 2004. The special thanks go to my advisor, Mariano Cilia, who has made all this possible. Finally, I’d like to thank to my family for all these years of support.

The theory of evolution links random variation and selection to incremental adaptation. In a different intellectual domain, learning theory links incremental adaptation (e.g., from positive and/or negative reinforcement) to intelligent behaviour. Specifically, learning theory explains how