A Mathematical Theory of System Information Flow

Abstract : The initial goal of this project was to study information flow in computational systems using techniques from information theory, domain theory andother areas of mathematics and computer science. Over time, the focus shifted toward a better understanding of random variables, in particular froma domain-theoretic perspective. The research focused more narrowly on the relationship between random variables, domain theory and related work on information theory. The results produced by the project include two new models for probabilistic computation. one of which models randomized algorithms and the other of which is suitable for analyzing crypto-protocols. The project also produced a new statistical testing regimen for evaluating empirical tests of quantum phenomena that have since been the basis for validating the first loophole free tests of nonlocality. Finally, the project applied Skorohod's Theorem to analyze the domain structure of certain domains, and conversely, produced a domain-theoretic proof of Skorohod's Theorem that also show every measure on countably-based coherent domains is the image of Haar measure on the Cantor set under a Scott-continuous mapping.