Abstract
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 S 12 . 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 ↦ 2i ((log(i+1) n)O(1) for i ≥ 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.
Supported by a Marie Curie Individual Fellowship #HPMF-CT-2000-00803 from the European Commission.
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Beckmann, A. (2002). Resolution Refutations and Propositional Proofs with Height-Restrictions. In: Bradfield, J. (eds) Computer Science Logic. CSL 2002. Lecture Notes in Computer Science, vol 2471. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-45793-3_40
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DOI: https://doi.org/10.1007/3-540-45793-3_40
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