Classic Nintendo Games are (Computationally) Hard? Greg Aloupis1??, Erik D. Demaine2, Alan Guo2???, and Giovanni Viglietta3 1 D´epartement d'Informatique, Universit´eLibre de Bruxelles,
[email protected] 2 MIT Computer Science and Artificial Intelligence Laboratory, 32 Vassar St., Cambridge, MA 02139, USA, fedemaine,
[email protected] 3 School of Electrical Engineering and Computer Science, University of Ottawa, Canada,
[email protected] Abstract. We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pok´emon.Our results apply to generalized versions of Super Mario Bros. 1, 3, Lost Levels, and Super Mario World; Donkey Kong Country 1{3; all Legend of Zelda games; all Metroid games; and all Pok´emon role-playing games. In addition, we prove PSPACE-completeness of the Donkey Kong Country games and several Legend of Zelda games. 1 Introduction A series of recent papers have analyzed the computational complexity of playing many different video games [1,4,5,6], but the most well-known classic Nintendo games have yet to be included among these results. In this paper, we analyze some of the best-known Nintendo games of all time: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pok´emon.We prove that it is NP-hard, and in some cases PSPACE-hard, to play generalized versions of most games in these series. In par- ticular, our NP-hardness results apply to the NES games Super Mario Bros., Su- per Mario Bros.: The Lost Levels, Super Mario Bros. 3, and Super Mario World (developed by Nintendo); to the SNES games Donkey Kong Country 1{3 (de- veloped by Rare Ltd.); to all Legend of Zelda games (developed by Nintendo);4 to all Metroid games (developed by Nintendo); and to all Pok´emonrole-playing games (developed by Game Freak and Creatures Inc.).5 Our PSPACE-hardness results apply to to the SNES games Donkey Kong Country 1{3, and to The ? Full paper available as arXiv:1203.1895, http://arXiv.org/abs/1203.1895 ?? Charg´ede Recherches du FNRS.