Symmetry within and between solutions

Details Symmetry within and between solutions Symmetry within and between solutions

2010-07-05

arxiv.org/abs/1007.0604v1

Computer Science

Artificial Intelligence

Keynote talk to appear in the Proceedings of the Eleventh Pacific Rim International Conference on Artificial Intelligence (PRI

Scientific paper

Symmetry can be used to help solve many problems. For instance, Einstein's famous 1905 paper ("On the Electrodynamics of Moving Bodies") uses symmetry to help derive the laws of special relativity. In artificial intelligence, symmetry has played an important role in both problem representation and reasoning. I describe recent work on using symmetry to help solve constraint satisfaction problems. Symmetries occur within individual solutions of problems as well as between different solutions of the same problem. Symmetry can also be applied to the constraints in a problem to give new symmetric constraints. Reasoning about symmetry can speed up problem solving, and has led to the discovery of new results in both graph and number theory.

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