Complexity Classes of Equivalence Problems Revisited

@article{Fortnow2011ComplexityCO,
  title={Complexity Classes of Equivalence Problems Revisited},
  author={Lance Fortnow and Joshua A. Grochow},
  journal={Inf. Comput.},
  year={2011},
  volume={209},
  pages={748-763}
}
To determine if two lists of numbers are the same set, we sort both lists and see if we get the same result. The sorted list is a canonical form for the equivalence relation of set equality. Other canonical forms arise in graph isomorphism algorithms. To determine if two graphs are cospectral (have the same eigenvalues), we compute their characteristic polynomials and see if they are equal; the characteristic polynomial is a complete invariant for cospectrality. Finally, an equivalence relation… CONTINUE READING