基于图的反馈驱动单词推断：面向Jotto问题的可扩展框架
Graph-Based Inference for Feedback-Driven Word Deduction: A Scalable Framework for the Jotto Problem
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- BML Munjal University（BML 穆贾尔大学）
- UPES Dehradun（UPES 德拉敦大学）
机构由 AI 辅助整理，请以论文原文为准。
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中文总结 AI 辅助
提出基于图的Jotto问题推断框架，用加权图表示单词空间，通过迭代约束传播缩小假设空间，支持变长及重复字母，实验发现迭代次数随词长对数减少。
中文摘要 AI 辅助
本文提出了一种基于Jotto问题的反馈驱动单词推断框架，并将问题空间表示为加权图，其中所有有效单词对应节点，边权重由两个单词之间的共同字母数量定义。最后，游戏过程被定义为一种迭代约束传播机制，其中反馈用于迭代地缩小图的不兼容空间，从而以结构化和可解释的方式促进假设空间的缩减。与现有方法通常将问题空间定义为固定长度同字母异序词不同，所提出的框架推广到可变长度单词（3至8个字母），并自然扩展到重复字母的情况，首次在统一框架内处理真实的Jotto问题实例。通过交互式实现和定性案例研究，分别讨论了所提出框架的适用性和求解器动态。在约3000个模拟游戏场景上进行的大量自动化测试发现了一种新颖的收敛行为：预期迭代次数随单词长度增加而减少。使用统计检验确认了强对数关系，并通过回归建模和拟合优度检验进行了验证。除了初始问题陈述外，该公式将图剪枝引入为一种具有可解释性的反馈驱动推断的可行范式，并关联到符号推理和交互式智能系统。
英文摘要
A feedback-based word deduction framework based on the Jotto problem is proposed, and the problem space is represented as a weighted graph where all valid words correspond to nodes, and the edge weight is defined by the number of common letters between the two words. Finally, the gameplay is defined as an iterative constraint propagation mechanism where feedback is used to iteratively narrow the incompatible space of the graph, facilitating the reduction of the hypothesis space in a structured and interpretable manner. In contrast to existing approaches, where the problem space is typically defined for fixed-length isograms, the proposed framework generalizes to variable-length words (between 3 and 8 letters) and naturally extends to repeated letter cases, facilitating the treatment of realistic Jotto problem instances within a unified framework for the first time. The proposed framework's applicability and solver dynamics are also discussed through an interactive implementation and a qualitative case study, respectively. Significant automated tests on approximately 3,000 simulated gameplay scenarios identify a novel convergence behavior: the expected number of iterations diminishes with increasing word length. A strong relationship is confirmed using statistical tests to verify a logarithmic relationship, which is also verified using regression modeling and goodness-of-fit tests. In addition to the initial problem statement, this formulation introduces graph pruning as a viable paradigm for feedback-driven inference with interpretability and its association with symbolic reasoning and interactive intelligent systems.
