Optimal proof systems imply complete sets for promise classes

@article{Kbler2003OptimalPS,
  title={Optimal proof systems imply complete sets for promise classes},
  author={Johannes K{\"o}bler and Jochen Messner and Jacobo Tor{\'a}n},
  journal={Inf. Comput.},
  year={2003},
  volume={184},
  pages={71-92}
}
A polynomial time computable function h : Σ* → Σ* whose range is a set L is called a proof system for L. In this setting, an h-proof for x ∈ L is just a string w with h(w) = x. Cook and Reckhow defined this concept in [13], and in order to compare the relative strength of different proof systems for the set TAUT of tautologies in propositional logic, they considered the notion of p-simulation. Intuitively, a proof system h' p-simulates h if any h-proof w can be translated in polynomial time… CONTINUE READING
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