Graph-Based Inference for Feedback-Driven Word Deduction: A Scalable Framework for the Jotto Problem

Abstract

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.