Abstract
A proof system for a language L is a function f such that Range(f) is exactly L. In this paper, we look at proof systems from a circuit complexity point of view and study proof systems that are computationally very restricted. The restriction we study is: they can be computed by bounded fanin circuits of constant depth (NC0), or of O(loglogn) depth but with O(1) alternations (poly log AC0). Each output bit depends on very few input bits; thus such proof systems correspond to a kind of local error-correction on a theorem-proof pair.
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