The paper analyzes the computational complexity of all 15 2D Super Mario platforming video games released to date. The authors prove that 13 of these games are PSPACE-hard, using reductions from the PSPACE-complete "reachability with planar door gadgets" problem. The door gadgets constructed vary across the games, taking advantage of unique mechanics in each title.
For the remaining 2 games, Super Mario Land and Super Mario Run, the authors show that they are at least NP-hard, using a different reduction framework. The authors note that these games lack mechanics that can be used to build the door gadgets required for PSPACE-hardness proofs.
The paper also discusses the challenges in bounding the complexity of these games, as many have mechanics that can generate an unbounded number of on-screen objects, potentially leading to undecidability. The authors leave this as an open problem for future work.
To Another Language
from source content
arxiv.org
Önemli Bilgiler Şuradan Elde Edildi
by MIT Hardness... : arxiv.org 04-17-2024
https://arxiv.org/pdf/2404.10380.pdfDaha Derin Sorular