摘要翻译：
目前，细胞神经网络(CNN)已在模拟计算机上并行实现，并呈现出快速发展的趋势。物理学家必须意识到，这种计算机适合于以优雅的方式解决实际重要的问题，而这些问题在经典数字体系结构上是极其缓慢的。本文将CNN用于格上NP难优化问题的求解。证明了所有单元参数可单独控制的CNN是二维伊辛型（Edwards-Anderson）自旋玻璃系统的模拟对应体。利用CNN计算机的特性，可以建立此类问题的快速优化方法。估算了在基于CNN的计算机上求解此类NP难优化问题所需的仿真时间，并与用模拟退火算法在普通数字计算机上所需的仿真时间进行了比较，结果是惊人的：CNN计算机比已有10×10格大小的数字计算机要快。现在实现的硬件是176*144尺寸。此外，采用CNN芯片来解决这些问题似乎没有技术上的困难，所需的本地控制有望在不久的将来得到充分发展。
---
英文标题：
《Cellular neural networks for NP-hard optimization problems》
---
作者：
M\'aria Ercsey-Ravasz (P\'eter P\'azm\'any Catholic University),
  Tam\'as Roska (P\'eter P\'azm\'any Catholic University), Zolt\'an N\'eda
  (Babes-Bolyai University)
---
最新提交年份：
2008
---
分类信息：

一级分类：Physics        物理学
二级分类：Disordered Systems and Neural Networks        无序系统与神经网络
分类描述：Glasses and spin glasses; properties of random, aperiodic and quasiperiodic systems; transport in disordered media; localization; phenomena mediated by defects and disorder; neural networks
眼镜和旋转眼镜；随机、非周期和准周期系统的性质；无序介质中的传输；本地化；由缺陷和无序介导的现象；神经网络
--
一级分类：Physics        物理学
二级分类：Statistical Mechanics        统计力学
分类描述：Phase transitions, thermodynamics, field theory, non-equilibrium phenomena, renormalization group and scaling, integrable models, turbulence
相变，热力学，场论，非平衡现象，重整化群和标度，可积模型，湍流
--

---
英文摘要：
  Nowadays, Cellular Neural Networks (CNN) are practically implemented in parallel, analog computers, showing a fast developing trend. Physicist must be aware that such computers are appropriate for solving in an elegant manner practically important problems, which are extremely slow on the classical digital architecture. Here, CNN is used for solving NP-hard optimization problems on lattices. It is proved, that a CNN in which the parameters of all cells can be separately controlled, is the analog correspondent of a two-dimensional Ising type (Edwards-Anderson) spin-glass system. Using the properties of CNN computers a fast optimization method can be built for such problems. Estimating the simulation time needed for solving such NP-hard optimization problems on CNN based computers, and comparing it with the time needed on normal digital computers using the simulated annealing algorithm, the results are astonishing: CNN computers would be faster than digital computers already at 10*10 lattice sizes. Hardwares realized nowadays are of 176*144 size. Also, there seems to be no technical difficulties adapting CNN chips for such problems and the needed local control is expected to be fully developed in the near future.
---
PDF链接：
https://arxiv.org/pdf/802.115