The Foundations of Computation and Complexity Theory over the Reals or an Arbitrary Ring

传统上，计算理论和计算 复杂性处理离散问题。 另一方面很多 计算问题以真实的数为自然域。 一 各种特设的方法和模型已被用来分析 在这个领域的复杂性问题，但与经典的情况下， 自然不变理论尚未出现。 这个项目是追求一个正式的理论基础， 计算和复杂性的实数，或任意环R。 它 结合了经典的递归函数理论和复杂性理论 主流代数分析和拓扑学

Classically, the theories of computation and computational complexity deal with discrete problems. On the other hand, many computational problems have the real numbers as natural domain. A variety of ad hoc methods and models have been employed to analyze complexity issues in this realm, but unlike the classical case, a natural and invariant theory has not yet emerged. This project is pursuing the foundations of a formal theory of computation and complexity over the reals, or an arbitrary ring R. It integrates classical recursive function theory and complexity theory with mainstream algebra, analysis and topology.