Monday, October 5, 2015

Lecture 21

Graph Non-Isomorphism is in AM
Proof in Section 3 of this paper.

We also showed that if co-NP is contained in AM then the polynomial-time hierarchy collapses to the second level. Combined these results show that if Graph Isomorphism is NP-complete then the polynomial-time hierarchy collapses. This is the best evidence we have that GI is not NP-complete.