2014
DOI: 10.1007/978-3-319-07890-8_4
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Abstract: We prove NP-hardness results for five of Nintendo's largest video game franchises: Mario, Donkey Kong, Legend of Zelda, Metroid, and Pokémon. Our results apply to generalized versions of Super Mario Bros. 1-3, The Lost Levels, and Super Mario World; Donkey Kong Country 1-3; all Legend of Zelda games; all Metroid games; and all Pokémon role-playing games. In addition, we prove PSPACE-completeness of the Donkey Kong Country games and several Legend of Zelda games.

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Cited by 36 publications
(80 citation statements)
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“…Our results follow a series of recent work on the computational complexity of video games, including the broad work of Forisek [For10] and Viglietta [Vig14] as well as the specific analyses of classic Nintendo games [ADGV15].…”
Section: Introductionsupporting
confidence: 68%
“…Our results follow a series of recent work on the computational complexity of video games, including the broad work of Forisek [For10] and Viglietta [Vig14] as well as the specific analyses of classic Nintendo games [ADGV15].…”
Section: Introductionsupporting
confidence: 68%
“…Also, for every (v, u) ∈ E, G has exactly σ((v, u)) copies of the directed edge (v, u). Because σ passes the above tests, G is weakly connected and satisfies equations (1) to (4), implying that it is Eulerian or semi-Eulerian. Therefore G has an Eulerian walk w from s to t. Such an Eulerian walk directly translates into a walk w on G from s to t that traverses each edge e ∈ E exactly σ(e) times.…”
Section: Instances Solvable In Npmentioning
confidence: 95%
“…For the PSPACE-hardness reduction, we apply a framework introduced in [11,Metatheorem 4.c], which has also appeared in [4]. The framework is based on a reduction from Quantified Boolean Formula involving a playercontrolled avatar, a starting location, an exit location, several paths, pressure plates and doors.…”
Section: Pspace-complete Instancesmentioning
confidence: 99%
“…We can always convert a gate with fan-in p to p−1 separate gates, each of fan-in 2, but this comes at the cost of increasing the depth by at least log p (achieved by arranging the replacement gates in a binary tree). Thus, if we require our circuits to have depth O (1), then any gate with fan-in ω(1) cannot be replaced in this way. Definition 4.…”
Section: Parameterized Complexitymentioning
confidence: 99%
“…This paper addresses the question of whether parameterized versions of Ricochet Robots and Atomix admit FPT algorithms as follows. Ricochet Robots and Atomix are: ( 1 ) FPT when parameterized by the sum of the number of agents and solution length (Section 3), ( 2 ) Hard for W[SAT], the highest class in the W-hierarchy (defined in Section 2), when parameterized by the number of agents, and ( 3 ) In W [1], the lowest class in the W-hierarchy, when parameterized by the length of solution (but unresolved as to whether they are in FPT or hard for W [1]). …”
Section: Introductionmentioning
confidence: 99%