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Pré-Publication, Document De Travail Année : 2024

Zeta Functions and the (Linear) Logic of Markov Processes

Résumé

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

hal-02458330 , version 1 (28-01-2020)
hal-02458330 , version 2 (24-02-2020)
hal-02458330 , version 3 (27-01-2021)
hal-02458330 , version 4 (07-11-2022)
hal-02458330 , version 5 (03-11-2023)
hal-02458330 , version 6 (06-04-2024)

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Thomas Seiller. Zeta Functions and the (Linear) Logic of Markov Processes. 2024. ⟨hal-02458330v6⟩
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