Building connections between theories of computing and physical systems

The theory and semantics of programming languages are typically formulated using abstract mathematical models that have no obvious connection to any physical theory. While this approach has a number of advantages, it does not generalize to complex nondiscrete systems, and it obscures the underlying mathematical connections between computational and physical theory. Moreover, it can lead to inaccurate models of more complex phenomena such as concurrency. In this paper, we describe the current directions and initial results of our efforts to build connections between programming language theory and semantics and physical theory. The first and most mature of these efforts aims to develop a denotational semantic model that expands upon the mathematical formulation of quantum systems to provide a denotational foundation for concurrent languages. The second effort aims to generalize the notion of type systems to a probability inference system based on Bayesian probability. The third and final effort aims to develop an understanding of the dynamics of concurrent processes, with the goal of reasoning about the real behavior of processes in greater detail. In each of these efforts, we aim to draw connections between computing and other scientific disciplines.