Speaker: Paolo Dini (University of Hertfordshire and London School of Economics)

Title: An algebraic form of emergence: interaction computing for software synthesis

Abstract: In this talk I will retrace the argument that over the past 10 years has led us to the biochemistry of the cell as the starting point for developing a model of self-organizing, biologically-inspired computing. We call this model Interaction Computing (IC) because it relies on interaction events to advance its algorithm(s) rather than on a clock. I will outline some of its architectural implications and will locate it within a wider order-construction framework spanning from biological evolution to traditional software engineering methodology. Our approach is based on the assumptions that (1) the self-organizing properties of cellular processes depend on their non-linear character, and (2) that such a bottom-up approach requires intrinsic structural constraints between the interacting entities. Therefore, we rely heavily on algebra in the form of Lie symmetry analysis of the systems of ODEs modelling cellular pathways, algebraic automata theory to analyse the structure of the finite-state automata models of the same pathways, and are exploring the Chevalley construction of (some of) the finite simple groups from semisimple Lie algebras as a possible formal link between them. We are also developing a category theory framework to find functors and adjunctions between these continuous and discrete dynamical system views of the problem, and the coalgebraic logic for a "digital biochemistry" specification language. Managing expectations: we are at the beginning of the second year of the 3-year BIOMICS EU project. We have not cracked the problem yet and I will not present a formal IC model, but we have laid the groundwork and in this talk I will discuss our latest insights and results.