Gaming Is a Hard Job, but Someone Has to Do It!

Viglietta, Giovanni

doi:10.1007/s00224-013-9497-5

Cited by 40 publications

(75 citation statements)

References 11 publications

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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: 69%

Mario Kart Is Hard

Bosboom¹,

Demaine²,

Hesterberg³

et al. 2016

Lecture Notes in Computer Science

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Abstract. Nintendo's Mario Kart is perhaps the most popular racing video game franchise. Players race alone or against opponents to finish in the fastest time possible. Players can also use items to attack and defend from other racers. We prove two hardness results for generalized Mario Kart: deciding whether a driver can finish a course alone in some given time is NP-hard, and deciding whether a player can beat an opponent in a race is PSPACE-hard.

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Section: Introductionsupporting

confidence: 69%

Mario Kart Is Hard

Bosboom¹,

Demaine²,

Hesterberg³

et al. 2016

Lecture Notes in Computer Science

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“…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%

Lemmings Is PSPACE-Complete

Viglietta

2014

Lecture Notes in Computer Science

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Abstract. Lemmings is a computer puzzle game developed by DMA Design and published by Psygnosis in 1991, in which the player has to guide a tribe of lemming creatures to safety through a hazardous landscape, by assigning them specific skills that modify their behavior in different ways. In this paper we study the optimization problem of saving the highest number of lemmings in a given landscape with a given number of available skills. We prove that the game is PSPACE-complete, even if there is only one lemming to save, and only Builder and Basher skills are available. We thereby settle an open problem posed by Cormode in 2004, and again by Forišek in 2010. However we also prove that, if we restrict the game to levels in which the available Builder skills are only polynomially many (and there is any number of other skills), then the game is solvable in NP. Similarly, if the available Basher, Miner, and Digger skills are polynomially many, the game is solvable in NP. Furthermore, we show that saving the maximum number of lemmings is APX-hard, even when only one type of skill is available, whatever this skill is. This contrasts with the membership in P of the decision problem restricted to levels with no "deadly areas" (such as water or traps) and only Climber and Floater skills, as previously established by Cormode.

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“…One of the earliest results in the area is that generalised chess is EXPTIME-complete (Fraenkel & Lichtenstein, 1981). Amongst other games to have been proved NP-complete or harder are the card solitaire games Klondike (Longpré & McKenzie, 2009), Freecell (Helmert, 2003) and Black Hole (Gent, Jefferson, Kelsey, Lynce, Miguel, Nightingale, Smith, & Tarim, 2007), the Sudoku puzzle (Takayuki & Takahiro, 2003), video games like Pac-Man (Viglietta, 2014), and casual games such as Minesweeper (Kaye, 2000), Candy Crush Saga and Bejeweled (Walsh, 2014;Guala, Leucci, & Natale, 2014). Many other games are surveyed by Kendall, Parkes, and Spoerer (2008) and by Demaine and Hearn (2009).…”

Section: Introductionmentioning

confidence: 99%

Complexity of n-Queens Completion

Gent

Jefferson

Nightingale

2017

jair

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The n-Queens problem is to place n chess queens on an n by n chessboard so that no two queens are on the same row, column or diagonal. The n-Queens Completion problem is a variant, dating to 1850, in which some queens are already placed and the solver is asked to place the rest, if possible. We show that n-Queens Completion is both NP-Complete and #P-Complete. A corollary is that any non-attacking arrangement of queens can be included as a part of a solution to a larger n-Queens problem. We introduce generators of random instances for n-Queens Completion and the closely related Blocked n-Queens and Excluded Diagonals Problem. We describe three solvers for these problems, and empirically analyse the hardness of randomly generated instances. For Blocked n-Queens and the Excluded Diagonals Problem, we show the existence of a phase transition associated with hard instances as has been seen in other NP-Complete problems, but a natural generator for n-Queens Completion did not generate consistently hard instances. The significance of this work is that the n-Queens problem has been very widely used as a benchmark in Artificial Intelligence, but conclusions on it are often disputable because of the simple complexity of the decision problem. Our results give alternative benchmarks which are hard theoretically and empirically, but for which solving techniques designed for n-Queens need minimal or no change.

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Gaming Is a Hard Job, but Someone Has to Do It!

Cited by 40 publications

References 11 publications

Mario Kart Is Hard

Mario Kart Is Hard

Lemmings Is PSPACE-Complete

Complexity of n-Queens Completion

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