  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 currently 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-hard. 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-hard. 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.
