Thomas Seiller - Zeta Functions and the (Linear) Logic of Markov Processes

lmcs:10303 - Logical Methods in Computer Science, August 29, 2024, Volume 20, Issue 3 - https://doi.org/10.46298/lmcs-20(3:18)2024
Zeta Functions and the (Linear) Logic of Markov ProcessesArticle

Authors: Thomas Seiller

    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.


    Volume: Volume 20, Issue 3
    Published on: August 29, 2024
    Accepted on: June 24, 2024
    Submitted on: November 15, 2022
    Keywords: Computer Science - Logic in Computer Science,Mathematics - Dynamical Systems,Mathematics - Logic,Mathematics - Probability
    Funding:
      Source : OpenAIRE Graph
    • Dynamical Systems and Computation: a logical approach; Funder: French National Research Agency (ANR); Code: ANR-22-CE48-0003
    • A Realizability Approach to Complexity Theory; Funder: European Commission; Code: 659920

    Classifications

    Mathematics Subject Classification 20201

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