Simulating Sudoku Solvers: A Comparative Study of Deterministic, Probabilistic and Learning-Based Approaches

Abstract

: While Sudoku is governed by simple rules, it represents a complex constraint-satisfaction problem ideal for simulating and evaluating the performance of intelligent agents. This study presents a simulation framework designed to evaluate the behavioral effectiveness of various automated solvers. Deterministic methods, such as backtracking and SAT solving, as well as probabilistic methods like Monte Carlo Tree Search and Deep Learning networks, were implemented and compared. Furthermore, we introduce AlphaSudoku, a hybrid simulation model that integrates probabilistic rules and strategic search. Through extensive experimentation across two thousand puzzles of varying difficulty levels, our results demonstrate that deterministic solvers maintain perfect reliability, achieving 100% success rates even on expert-level puzzles. While AlphaSudoku emerges as an effective balance between computational efficiency and solving accuracy, purely probabilistic methods exhibit significant limitations when confronted with higher-difficulty puzzles. These findings highlight the robustness of traditional symbolic methods, while also revealing the potential of hybrid and learning-based approaches in scenarios requiring adaptability and scalability.