Highly Influenced

@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} }

- Published 2012 in computational complexity
DOI:10.1007/s00037-012-0044-6

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.