Using Small MUSes to Explain How to Solve Pen and Paper Puzzles

Abstract

Pen and paper puzzles like Sudoku, Futoshiki and Skyscrapers are hugely popular. Solving such puzzles can be a trivial task for modern AI systems. However, most AI systems solve problems using a form of backtracking, while people try to avoid backtracking as much as possible. This means that existing AI systems do not output explanations about their reasoning that are meaningful to people. We present DEMYSTIFY, a tool which allows puzzles to be expressed in a high-level constraint programming language and uses MUSes to allow us to produce descriptions of steps in the puzzle solving. We give several improvements to the existing techniques for solving puzzles with MUSes, which allow us to solve a range of significantly more complex puzzles and give higher quality explanations. We demonstrate the effectiveness and generality of DEMYSTIFY by comparing its results to documented strategies for solving a range of pen and paper puzzles by hand, showing that our technique can find many of the same explanations.

Sudoku Assistant – an AI-Powered App to Help Solve Pen-and-Paper Sudokus

“…A non-exhaustive list of works (Reeson et al 2007;Caine and Cohen 2007), showcase (interactive) tutoring systems using the Sudoku puzzle, for instance, to teach consistency propagation algorithms in Constraint Programming (Howell et al 2018). Other works rely on Minimal Unsatisfiable Subsets (MUS) to compute a minimal subset of constraints and facts that can be used to derive new information (Bogaerts, Gamba, and Guns 2021;Espasa et al 2021). Few works have considered optimizing MUSs with respect to a given cost-function.…”

Rule-based explaining module: Enhancing the interpretability of recurrent relational network in Sudoku solving

“…However, the method's dependence on a potentially inaccurate model of human mental effort could result in explanations that are not entirely accurate. Another approach, Demystify, introduced by Espasa et al, provides step-by-step explanations for solving various pen-and-paper puzzles, including Sudoku [5]. It utilizes Minimal Unsatisfiable Subsets (MUSes) to solve puzzles through logical deduction, identifying essential puzzle components for progress.…”

“…The cross-entropy loss function, defined in formula (5), is used to optimize the model's performance during training. The target digits, represented by y = y 1 , y 2 , y 3 , .…”