Classic Nintendo games are (computationally) hard

Aloupis, Greg; Demaine, Erik D.; Guo, Alan; Viglietta, Giovanni

doi:10.1016/j.tcs.2015.02.037

Cited by 26 publications

(23 citation statements)

References 4 publications

(14 reference statements)

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“…Please note that for the sake of our proofs we consider a game containing elements with pseudorandom behaviour/physics to still be deterministic, as long as the random seed used to define them can be encoded in a polynomial number of bits (i.e. not truly stochastic) [1]. Table 1 shows how altering these two factors within the Angry Birds game affects its complexity.…”

Section: Number Of Birdsmentioning

confidence: 99%

“…The computational complexity of different video games has been the subject of much investigation over the past decade. However, this has mostly been carried out on traditional style platformers [1,2] or primitive puzzle games [3,4]. In this paper, we analyse the complexity of playing different variants of the video game Angry Birds, which is a sophisticated physics-based puzzle game with a semi-realistic and controlled environment [5].…”

Section: Introductionmentioning

confidence: 99%

“…Video games have been the subject of much prior research on computational complexity, with many papers proving specific games to be either NP-hard or PSPACE-complete. Examples of past proofs for NP-hardness include games such as Pac-Man [4], Lemmings [16], Portal [17], Candy Crush [18], Bejeweled [19], Minesweeper [20], Tetris [21], and multiple classic Nintendo games [1]. Proofs of PSPACE-completeness have also been described for games such as Mario Bros. [22], Doom [4], Pokémon [1], Rush Hour [23], Mario Kart [24] and Prince of Persia [2].…”

Section: Introductionmentioning

confidence: 99%

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The computational complexity of Angry Birds

Stephenson

Renz

2020

Artificial Intelligence

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The physics-based simulation game Angry Birds has been heavily researched by the AI community over the past five years, and has been the subject of a popular AI competition that is being held annually as part of a leading AI conference. Developing intelligent agents that can play this game effectively has been an incredibly complex and challenging problem for traditional AI techniques to solve, even though the game is simple enough that any human player could learn and master it within a short time. In this paper we analyse how hard the problem really is, presenting several proofs for the computational complexity of Angry Birds. By using a combination of several gadgets within this game's environment, we are able to demonstrate that the decision problem of solving general levels for different versions of Angry Birds is either NP-hard, PSPACE-hard, PSPACE-complete or EXPTIME-complete. Proof of NP-hardness is by reduction from 3-SAT, whilst proof of PSPACE-hardness is by reduction from True Quantified Boolean Formula (TQBF).Proof of EXPTIME-hardness is by reduction from G2, a known EXPTIME-complete problem similar to that used for many previous games such as Chess, Go and Checkers. To the best of our knowledge, this is the first time that a single-player game has been proven EXPTIME-complete. This is achieved by using stochastic game engine dynamics to effectively model the real world, or in our case the physics simulator, as the opponent against which we are playing. These proofs can also be extended to other physics-based games with similar mechanics.

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Section: Number Of Birdsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The computational complexity of Angry Birds

Stephenson

Renz

2020

Artificial Intelligence

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“…Understanding the computational complexity of games has raised some interest in the computer science community, and many games have been proven to be complete for NP or co-NP. Examples include Minesweeper [14,18], SET [15], Hanabi [3], Nintendo games [2] and Candy Crush [9,20].…”

Section: Introductionmentioning

confidence: 99%

NP-completeness of the game KingdominoTM

Nguyen

Perrot

Vallet

2020

Theoretical Computer Science

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Kingdomino TM is a board game designed by Bruno Cathala and edited by Blue Orange since 2016. The goal is to place 2 × 1 dominoes on a grid layout, and get a better score than other players. Each 1 × 1 domino cell has a color that must match at least one adjacent cell, and an integer number of crowns (possibly none) used to compute the score. We prove that even with full knowledge of the future of the game, in order to maximize their score at Kingdomino TM , players are faced with an NP-complete optimization problem. Computational complexity of games and dominoesKingdomino TM has been studied in [8], where the authors compare different strategies to play the game, via numerical simulations.

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“…The simplicity of early video games has led to their use as model systems for 47 reinforcement learning [13] and computational complexity research [14]. The video game 48 system ("whole animal") has a well defined output in each of the three behavioral 49 conditions (games).…”

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confidence: 99%

Could a Neuroscientist Understand a Microprocessor?

Jonas

Kording

2016

Preprint

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There is a popular belief in neuroscience that we are primarily data limited, and that producing large, multimodal, and complex datasets will, with the help of advanced data analysis algorithms, lead to fundamental insights into the way the brain processes information. These datasets do not yet exist, and if they did we would have no way of evaluating whether or not the algorithmically-generated insights were sufficient or even correct. To address this, here we take a classical microprocessor as a model organism, and use our ability to perform arbitrary experiments on it to see if popular data analysis methods from neuroscience can elucidate the way it processes information. Microprocessors are among those artificial information processing systems that are both complex and that we understand at all levels, from the overall logical flow, via logical gates, to the dynamics of transistors. We show that the approaches reveal interesting structure in the data but do not meaningfully describe the hierarchy of information processing in the microprocessor. This suggests current analytic approaches in neuroscience may fall short of producing meaningful understanding of neural systems, regardless of the amount of data. Additionally, we argue for scientists using complex non-linear dynamical systems with known ground truth, such as the microprocessor as a validation platform for time-series and structure discovery methods. Author SummaryNeuroscience is held back by the fact that it is hard to evaluate if a conclusion is correct; the complexity of the systems under study and their experimental inaccessability make the assessment of algorithmic and data analytic technqiues challenging at best. We thus argue for testing approaches using known artifacts, where the correct interpretation is known. Here we present a microprocessor platform as one such test case. We find that many approaches in neuroscience, when used naïvely, fall short of producing a meaningful understanding.

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Classic Nintendo games are (computationally) hard

Cited by 26 publications

References 4 publications

The computational complexity of Angry Birds

The computational complexity of Angry Birds

NP-completeness of the game KingdominoTM

Could a Neuroscientist Understand a Microprocessor?

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