论文标题
Zeta功能和Markov进程的（线性）逻辑
Zeta Functions and the (Linear) Logic of Markov Processes
论文作者
论文摘要
作者介绍了被称为“交互图”的线性逻辑模型，该模型概括了Girard的各种相互作用构造几何形状。在这项工作中，我们确定了这些模型如何基本上依赖于Zeta函数与执行程序之间的深厚连接，以表达为Cocycle。这首先在图形的简单情况下首先显示，然后开始提起动态系统。然后，我们专注于概率模型，然后解释相互作用图中使用的图形概念如何捕获一类天然的亚马科夫过程。然后，我们扩展了ZETA函数的真实性结构和概念，以在所有（离散时间）subarkov过程的集合上提供二阶线性逻辑的真实性模型。
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.
