Is Quadratic Arithmetic Program NP-complete? I'm reading this paper: Quadratic Span Programs and Succinct NIZKs without PCP
Is QAP NP-complete? as same as QSP?
QAP, like QSP, are a characterization of NP. They naturally capture arithmetic programs. Their advantage over QSP is that they lead to more efficient SNARGs for statements whose verification procedure is compactly represented by an arithmetic circuit. They have at least the same power, and you can represent the verification algorithm of arbitrary NP languages (hence also NP-complete languages) using them. Note that they are a computation model, not a language, so it does not mean anything to say that QAPs (or QSPs) are NP-complete - but they do capture all of NP.