The computational complexity of Angry Birds

Abstract

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.

Classifying Celeste as NP Complete

“…This work serves as a stepping stone towards analysing computational complexity of more sophisticated interactive systems and increases the scope of video games that have been studied within this field. Further work involves investigating the hardness of platformers with more involved mechanics, similar to what has been done on analysing the complexity of the popular arcade game Angry Birds [8]. We are hopeful that our work opens up new directions to understand the relationship between the mechanics of interactive systems and computational complexity.…”

Hardness of Modern Games

“…Cut the Rope is a physics based game, hence the gadgets we use are unsual, in particular we need to handle physics problems, such as speed adjusting. Angry birds is another physics based games which was recently shown to be NP-Hard [14]. Hexiom is a puzzle game, however a straight forward construction of local constrains to simulate circuit components is tricky.…”

The Role of Big Data in Industrial (Bio)chemical Process Operations

“…They are particularly well-suited to play relatively complicated video games such as Super Mario, 77 whereas more recent video games with less deterministic gaming engines, such as Angry Birds, have been rather challenging. 78 These algorithms are somewhat similar to classic closed-loop process control concepts as they are trained to meet targets and to maximize an objective. They represent another promising area of research that has been exploited in a limited manner in closed-loop control.…”

“…RL utilizes agents that learn a strategy to maximize rewards. They are particularly well-suited to play relatively complicated video games such as Super Mario, whereas more recent video games with less deterministic gaming engines, such as Angry Birds, have been rather challenging . These algorithms are somewhat similar to classic closed-loop process control concepts as they are trained to meet targets and to maximize an objective.…”