SNARKs based on Linear PCP have the shortest proof size known today
PCP is an idealized model that can be realized in practice using a vector commitment scheme
Linear PCP is a generalization of PCP
The computation trace c of a QAP only includes inputs to the circuit and the output of all multiplication gates in the circuit
The setup phase of the QAP to SNARK construction discussed in lecture 9 has O(mn) complexity as it needs to evaluate O(m) polynomials of degree n
Both setup and prover time in Groth16 are independent of the number of addition gates
The set Omega is chosen as the set of n-th roots of unity to improve verifier complexity of the QAP to SNARK construction
Circuit-specific trusted setup of the SNARK construction discussed in lecture 9 (not Groth16) can be converted to a universal trusted setup by computing circuit-specific global parameters from powers of tau
