Holographic reduction, interpolation and hardness

@article{Cai2012HolographicRI,
  title={Holographic reduction, interpolation and hardness},
  author={Jin-Yi Cai and Pinyan Lu and Mingji Xia},
  journal={computational complexity},
  year={2012},
  volume={21},
  pages={573-604}
}
We introduce the method of proving complexity dichotomy theorems by holographic reductions. Combined with interpolation, we present a unified strategy to prove #P-hardness. Specifically, we prove a complexity dichotomy theorem for a class of counting problems on 2–3 regular graphs expressible by Boolean signatures. For these problems, whenever a holographic reduction followed by interpolation fails to prove #P-hardness, we can show that the problem is solvable in polynomial time.