普适计算“几乎肯定”是混沌的
Universal Computation Is 'Almost Surely' Chaotic
摘要：
已知不动点迭代对于其参数范围内的某些值会产生混沌。图灵机是不动点迭代，这是一个既定的事实。然而，由于这些机器在整数空间中运行，混沌系统的标准概念并不适用于它们。将图灵机的状态空间从整数空间变换到有理空间，可以适当地建立混沌动力学的条件。进一步推导出，给定随机输入，由通用图灵机执行的计算将“几乎肯定”是混沌的。
英文摘要：
Fixed point iterations are known to generate chaos, for some values in their parameter range. It is an established fact that Turing Machines are fixed point iterations. However, as these Machines operate in integer space, the standard notions of a chaotic system is not readily applicable for them. Changing the state space of Turing Machines from integer to rational space, the condition for chaotic dynamics can be suitably established, as presented in the current paper. Further it is deduced that, given random input, computation performed by a Universal Turing Machine would be 'almost surely' chaotic.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
