Topological Kleene Field Theories as a model of computation
Ángel González-Prieto, Eva Miranda and Daniel Peralta-Salas
在这篇文章中,我们建立了计算场理论的基础,我们将其术语为拓扑Kleene场理论(TKFT),灵感来自Stephen Kleene关于部分递归函数的开创性工作,并与拓扑场理论绘制相似之处。 我们的核心结果表明,任何可计算函数都可以通过具有良好本地属性的向量场的平滑波纹上的流来模拟,为图灵机器设置计算的替代模型。 因此,我们确定一个可计算函数可以在一个动态系统的单一操作中完全实现,这与以前的计算被编码为迭代过程的工作不同。 可计算函数的输出直接出现,为加速计算物理实现的潜在应用奠定了基础。
In this article, we establish the foundations of a computational field theory, which we term Topological Kleene Field Theory (TKFT), inspired by Stephen Kleene's seminal work on partial recursive functions and drawing parallels with Topological Field Theory. Our central result shows that any computable function can be simulated by the flow on a smooth bordism of a vector field with good local properties, setting an alternative model of computation to Turing machines. We thus establish that a com...
