Fill-a-Pix Puzzle as a SAT Problem

Abstract

Fill-a-Pix Puzzle is a Picture Logic Puzzle that has not been solved as a SAT Problem as well as there is no SAT Conjunctive Normal Form (CNF) Encoding Method to solve this puzzle yet. There are several practical SAT problems in various fields such as Artificial Intelligence (AI), Automatic Theorem Proving, Circuit Design, etc. Fill-a-Pix puzzle is also one of the SAT problems. This research proposes the SAT CNF Encoding Method to solve Fill-a-Pix Puzzle as a SAT Problem using SAT Solvers. The proposed SAT CNF Encoding Method will be executed on different standard SAT solvers – MiniSAT, CryptoMiniSAT and RSAT. The evaluation is presented regarding the CPU Execution Times of each solver for executing the proposed SAT CNF Encoding, the Number of Variables and Clauses produced by the proposed SAT CNF Encoding as well as the Comparison of Fill-a-Pix Puzzle with the other Similar Puzzles such as Sudoku and Slitherlink based on the Number of Variables and Clauses produced by the proposed SAT CNF Encoding when executing Puzzle Sizes above 50 × 50.