Propagation Networks: A Flexible and Expressive Substrate for Computation

Abstract

I propose a shift in the foundations of computation. Practically all ideas of general-purpose computation today are founded either on execution of sequences of atomic instructions, i.e., assembly languages, or on evaluation of tree-structured expressions, i.e., most higher level programming languages. Both have served us well in the past, but it is increasingly clear that we need something more. I suggest that we can build general-purpose computation on propagation of information through networks of stateful cells interconnected with stateless autonomous asynchronous computing elements. Various forms of this general idea have been used with great success for various special purposes; perhaps the most immediate example is constraint propagation in constraint satisfaction systems. These special-purpose systems, however, are all complex and all different, and neither compose well, nor interoperate well, nor generalize well. A foundational layer is missing. The key insight in this work is that a cell should not be seen as storing a value, but as accumulating information about a value. The cells should never forget information -- such monotonicity prevents race conditions in the behavior of the network. Monotonicity of information need not be a severe restriction: for example, carrying reasons for believing each thing makes it possible to explore but thenpossibly reject tentative hypotheses, thus appearing to undo something, while maintaining monotonicity. Accumulating information is a broad enough design principle to encompass arbitrary computation. The object of this dissertation is therefore to architect a general-purpose computing system based on propagation networks; to subsume expression evaluation under propagation just as instruction execution is subsumed under expression evaluation; to demonstrate that a general-purpose propagation system can recover all the benefits that have been derived from special-purpose propagation systems, allow them to compose andinteroperate, and offer further expressive power beyond what we have known in the past; and finally to contemplate the lessons that such a fundamental shift can teach us about the deep nature of computation.