Separating the polynomial-time hierarchy by oracles
Proc. 26th annual symposium on Foundations of computer science
Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Lower bounds to the size of constant-depth propositional proofs
Journal of Symbolic Logic
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
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Height restricted resolution (proofs or refutations) is a natural restriction of resolution where the height of the corresponding proof tree is bounded. Height restricted resolution does not distinguish between tree- and sequence-like proofs. We show that polylogarithmic-height resolution is strongly connected to the bounded arithmetic theory S21 (驴). We separate polylogarithmic-height resolution from quasi-polynomial size tree-like resolution.Inspired by this we will study infinitely many sub-linear-height restrictions given by functions n 驴 2i (log(i+1) n)O(1)) for i 驴 0. We show that the resulting resolution systems are connected to certain bounded arithmetic theories, and that they form a strict hierarchy of resolution proof systems. To this end we will develop some proof theory for height restricted proofs.