Maybe Interactive, Not Zero-Knowledge, Arguments of Knowledge zkSNARK is a technique composed with the following features:


zk: zero-knowledge
S: Succinct
N: Non-interactive
ARK: ARgument of Knowledge


Everywhere I look on the web for material on cryptographic arguments of knowledge I find techniques that mush these four features together. I am only interested in feature 4, that is a technique with no conditions on features 1, 2, or 3, for Alice to prove to Bob that she correctly performed a computation without Bob needing to perform the computation. Could I find literature under a more commonly used name for this technique than 'argument of knowledge'? Can you please point me to some literature on this technique?

I am curious which of the 4 features are at the core of the research in this area. Is it feature 1 that makes these cryptographic techniques so hard? or features 2 or 3? If the difficulty of current research is in solving a combination of features 1, 2, and 3, then shouldn't there exist simpler, more successful techniques that only need to solve feature 4? If so, I'd like to learn about these techniques. Ideally I'd get a response like "sure, if you don't need features 1, 2, or 3, simply ...".
The zero-knowledge property is not the core feature, in the sense that it's already very challenging to come up with a construction satisfying 2-4, and once it's done, adding zero-knowledge usually comes almost for free.

The property 4 is necessary, as it is implied by the property 3: if you want succinctness, you cannot hope to get unconditional soundness. The intuition between this is that if we have a proof of size $n$ for (say) 3-SAT, then we can slove 3-SAT in time $2^n$, by doing exhaustive search over possible proofs (the formal result is a bit more involved as it also considers interactive proofsm but that's the main idea). Therefore, $n$ cannot be much smaller than the witness size, otherwise we would get a subexponential time algorithm for 3-SAT (which would be a major breakthrough).

The property 2 is essentially the one you want to keep: succinctness usually means that the size of the proof and the computation time of the verifier are sublinear in the witness size. And this is exactly what is hard to get :)

Eventually, non-interactivity is usually not the core issue if you are ok with working in the random oracle model - although that's not always the case, most constructions of succinct proofs can be made non-interactive in the random oracle model.

From your question, I guess that what you are looking for is not a succinct proof for all NP language, but only for proofs of languages in P, where the verifier could in principle redo the entire computation himself, but this would be too expensive. Proving correct computation is easier than proving all statements in NP. This was studied a lot (I'm giving keywords here) in the context of delegation of computation. I think one of the seminal papers in this area (you can also look via Google Scholar the papers that cite it) is this one. A more recent, really cool paper in this area is this one. If you provide us more details about the exact specifications of your problem, I might also be able to give you more pointers; delegation is an active research area, with many papers providing efficient solutions in many settings.

Summing up, if you only want succinctness and languages in P, this is indeed easier than building a zk-snark for all of NP, but that remains far from easy.