Generating and solving the LIGHTS OUT! game in first order logic

We compare here declarative approaches to model the LIGHTS OUT! game and its friends in First Order Logic (FOL). First, we solve the game using: (i) planning in FOL and (ii) a model finder for finite domains, for which we rely on Prover9 and Mace4. Second, we show how LIGHTS OUT! puzzles can be automatically generated by reasoning on finite models of FOL theories. We designed three solutions: (i) using a LIGHTS OUT! game solver in FOL, (ii) using linear algebra and a model generator, and (iii) improving the linear algebra-based method by decreasing the domain size. Third, we show how declarative knowledge can be reused to solve and generate different extensions of the LIGHTS OUT! game. We experimentally compare the proposed declarative methods and we discuss some extensions of theLIGHTS OUT! game.