Zeta Functions and the (Linear) Logic of Markov Processes

Abstract

The author introduced models of linear logic known as ''Interaction Graphs''which generalise Girard's various geometry of interaction constructions. Inthis work, we establish how these models essentially rely on a deep connectionbetween zeta functions and the execution of programs, expressed as a cocycle.This is first shown in the simple case of graphs, before begin lifted todynamical systems. Focussing on probabilistic models, we then explain how thenotion of graphings used in Interaction Graphs captures a natural class ofsub-Markov processes. We then extend the realisability constructions and thenotion of zeta function to provide a realisability model of second-order linearlogic over the set of all (discrete-time) sub-Markov processes