一种使用连续存储带的计算机器
A computing machinery using a continuous memory tape
AI总结：
提出一种利用连续存储带和频域调制求解子集和问题的计算机器，其信号生成可在多项式时间内完成，但读取特定和值仍需依赖专用硬件实现。
摘要：
通过考虑每个单元对应一个整数从而对应一个可能和的离散带，利用移位和逐元素求和，可以为子集和问题（一个NP完全问题，也是本研究的基石应用）给出一个伪多项式解。通过将每个可能的和视为频带上的单一频率脉冲，该机器可以在符号上扩展到连续情况。在这种情况下，与余弦的乘法对应于通信系统中的调制移位操作。初步实验表明，信号生成从而解空间计算可以在多项式时间内完成。然而，读取特定频率（和值）处的值存在问题，即目前无法在多项式时间内模拟。专用硬件实现可能是一种解决方案，其中基于电路和无线版本都可以尝试。还给出了一种多项式表示，声称类似于图灵机的带。还讨论了子集和问题的有理数和实数版本，其中有理数版本的问题映射到0-1范围内，具有特定的True值模式。尽管这种机器可能不完全等价于非确定性图灵机，但它可能有助于非确定性通用图灵机的实现。它可能为计算机器、信息处理和模式识别领域的理论和实践考虑铺平道路。
英文摘要：
By considering a discrete tape where each cell corresponds to an integer, thus to a possible sum, a pseudo-polynomial solution can be given to subset sum problem, which is an NP-complete problem and a cornerstone application for this study, using shifts and element-wise summations. This machinery can be extended symbolically to continuous case by thinking each possible sum as a single frequency impulse on the frequency band. Multiplication with a cosine in this case corresponds to the shifting operation as modulation in communication systems. Preliminary experimentation suggests that signal generation thus solution space calculation can be done in polynomial time. However, reading the value at a specific frequency (sum value) is problematic, namely cannot be simulated in polynomial time currently. Dedicated hardware implementation might be a solution, where both circuit-based and wireless versions might be tried out. A polynomial representation is also given that is claimed to be analogous to a tape of a Turing machine. Both rational and real number versions of the subset sum problem are also discussed, where the rational version of the problem is mapped to 0-1 range with specific patterns of True values. Although this machinery may not be totally equivalent to a non-deterministic Turing machine, it may be helpful for non-deterministic universal Turing machine actualization. It may pave way to both theoretical and practical considerations that can help computing machinery, information processing, and pattern recognition domains in various ways.
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。
