In this paper we investigate the following two questions:

Q1: Do there exist optimal proof systems for a given language L?Q2: Do there exist complete problems for a given promise class C?

For concrete languages L (such as TAUT or SAT and concrete promise classes C (such as NP coNP, UP, BPP, disjoint NP-pairs etc.), these questions have been intensively studied during the last years, and a number of characterizations have been obtained. Here we provide new characterizations for Q1 and Q2 that apply to almost all promise classes \C and languages L, thus creating a unifyingframework for the study of these practically relevant questions.

While questions Q1 and Q2 are left open by our results, we show that they receive affirmative answers when a small amount of advice is available in the underlying machine model. This continues a recent line of research on proof systems with advice started by Cook and Krajicek.