arXiv:2608.24742cs.LOcs.CL2026-08

用卡片自动编程的硬件图灵机,可自主运行复杂计算。

Design and Empirical Characterization of a Hardware-Realized Turing Machine with Automated Card-Based Programming

  • 用卡片读取和步进电机实现全自动状态转移与纸带控制
  • 卡片识别准确率从75%提升至90%,全系统输出与软件模拟完全一致
  • 适合对计算理论、硬件实现感兴趣的师生和创客

物理实现的图灵机仍很罕见,现有机电模型或机械逻辑游戏通常需人工干预才能推进每一步或重置状态表,限制了其只能进行短时演示,无法实现自主长程序运行。本文提出一种可自主执行多步计算、通过光学穿孔卡实现可编程输入的硬件图灵机。系统采用Arduino Mega处理状态转移逻辑,双NEMA 17步进电机驱动纸带双向移动,红外反射传感器检测符号,基于ESP32-CAM的光学穿孔卡读取器实现状态表自动加载。在非均匀光照下,采用广度优先搜索填充分割算法结合局部自适应阈值替代固定全局阈值,受限于ESP32-CAM微控制器内存与库资源,使20张卡测试集的卡片解码准确率从75%提升至90%(机械压平后达100%)。机械性能评估显示:制造精度±0.15 mm,齿轮齿条定位误差低于0.3 mm(50次试验),满载电压稳定性在±0.2 V内。端到端计算经并行软件模拟器tlang验证,所有硬件输出均与模拟参考结果完全一致。该系统通过自主运行、可编程光学输入及对机械、光学与计算性能的量化评估,超越了以往物理图灵机演示。

原文摘要 · Abstract (English)

Physical implementations of Turing Machines remain rare, and existing electromechanical demonstrators and mechanical logic games typically require manual operator intervention, either to trigger each computational step or to reconfigure the state table, or both. This restricts prior physical models to short, operator-paced demonstrations and prevents autonomous execution of extended computations. This paper addresses that gap with a hardware Turing Machine that enables autonomous multi-step execution and reprogrammable optical input without manual intervention between programs. The system integrates an Arduino Mega for state-transition logic, dual NEMA 17 stepper motors for bidirectional tape actuation, infrared reflectance sensors for symbol detection, and an ESP32-CAM-based optical punched-card reader for automated state-table loading. Hole detection under non-uniform illumination used a Breadth-First Search flood-fill algorithm with local adaptive thresholding rather than fixed global thresholding, driven by the memory and library constraints of the ESP32-CAM's microcontroller environment; this improved card-decoding accuracy from 75% to 90% (100% with mechanical card flattening) on a 20-card test set. Mechanical evaluation showed fabrication accuracy of +/-0.15 mm, rack-and-pinion positional error below 0.3 mm across 50 trials, and voltage supply stability within +/-0.2 V under full system load. End-to-end computation was validated against a parallel software simulator (tlang), with all hardware outputs matching the simulated reference exactly across multiple test programs. The system advances prior physical Turing Machine demonstrations through autonomous execution, reprogrammable optical input, and quantitative evaluation of its mechanical, optical, and computational performance.

图灵机硬件实现光学输入自动化

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