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

Abstract: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.

Logic in Computer Science (cs.LO); Computation and Language (cs.CL)

arXiv:2608.24742 [cs.LO]

(or arXiv:2608.24742v1 [cs.LO] for this version)

https://doi.org/10.48550/arXiv.2608.24742 Focus to learn more arXiv-issued DOI via DataCite (pending registration)

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