Fillmat is NP-Complete and ASP-Complete

Abstract

We study the computational complexity of a packing puzzle Fillmat, which is a type of pencil-and-paper puzzles made by Japanese puzzle publisher Nikoli. We show that the problem to decide if a given instance of Fillmat has a solution is NP-complete by a reduction from the circuit-satisfiability problem (Circuit-SAT). Our reduction is carefully designed so that we can also prove ASP-completeness of the another-solution-problem.