初等复杂性与von Neumann代数
Elementary Complexity and von Neumann Algebras
摘要：
在本文中，我们将展示如何使用来自冯诺依曼代数核心的概念来实现隐式复杂性模型的构建。也就是说，我们的目标是获得理解的经典计算的超有限$\mathrm{II}_1$因子，从卡尔马递归函数类。更多的方法，我们解决的问题，找到正确的角度来看，在算子代数的计算和组合方面之间的新关系。离散不变量的丰富结构可以提供一种数学设置，能够阐明一些基本的组合现象，这些现象是我们理解复杂性的基础。
英文摘要：
In this paper, we show how a construction of an implicit complexity model can be implemented using concepts coming from the core of von Neumann algebras. Namely, our aim is to gain an understanding of classical computation in terms of the hyperfinite $\mathrm{II}_1$ factor, starting from the class of Kalmar recursive functions. More methodologically, we address the problem of finding the right perspective from which to view the new relation between computation and combinatorial aspects in operator algebras. The rich structure of discrete invariants may provide a mathematical setting able to shed light on some basic combinatorial phenomena that are at the basis of our understanding of complexity.
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