In a Sigma-protocol, the steps are (1) commitment, (2) challenge, and (3) response. In general, the prover has a statement and witness that they can use to compute the commitment step. But in some cases (like Schnorr or equality of two discrete logarithms) the prover doesn't use the statement or witness in the first step.
Are there more general Sigma-protocols that have this delayed input property, not just ones based on discrete log or other algebraic problems? What about, e.g., Graph Hamiltonicity?