Graph automorphism problem ( GA) of determining whether a graph has a nontrivial automorphism is a good candidate for a problem in NP-intermediate. I'm looking for references that study the certificate complexity of graph non-automorphism (GNA= {G| G is rigid or asymmetric graph}). What is the best known lower bound on the length of certificates that proves a graph is rigid ($G \in GNA$)? Also, Is there a plausible conjecture that prohibits sub-exponential certificates for Co-NP-complete problems (analogues to ETH)?
Best lower bound for proof complexity of graph non-automorphism problem
cc.complexity theory;graph isomorphism;proof complexity;automorphism