• Corpus ID: 246015566

Detecting danger in gridworlds using Gromov's Link Condition

@article{Burns2022DetectingDI,
  title={Detecting danger in gridworlds using Gromov's Link Condition},
  author={Thomas F Burns and Robert Tang},
  journal={ArXiv},
  year={2022},
  volume={abs/2201.06274}
}
Gridworlds have been long-utilised in AI research, particularly in reinforcement learning, as they provide simple yet scalable models for many real-world applications such as robot navigation, emergent behaviour, and operations research. We initiate a study of gridworlds using the mathematical framework of reconfigurable systems and state complexes due to Abrams, Ghrist & Peterson. State complexes represent all possible configurations of a system as a single geometric space, thus making them… 
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48 References

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