  It is already shown that a Boolean function for a NP-complete problem can be
computed by a polynomial-sized circuit if its variables have enough number of
automorphisms. Looking at this previous study from the different perspective
gives us the idea that the small number of automorphisms might be a barrier for
a polynomial time solution for NP-complete problems. Here I show that by
interpreting a Boolean circuit as a graph, the small number of graph
automorphisms and the large number of subgraph automorphisms in the circuit
establishes the exponential circuit lower bound for NP-complete problems. As
this strategy violates the largeness condition in Natural proof, this result
shows that P!=NP without any contradictions to the existence of pseudorandom
functions.
