Proof complexity modulo the Polynomial Hierarchy: understanding alternation as a source of hardness
Chen, Hubie (2017) Proof complexity modulo the Polynomial Hierarchy: understanding alternation as a source of hardness. ACM Transactions on Computation Theory 9 (3), ISSN 1942-3454.
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Abstract
We present and study a framework in which one can present alternation-based lower bounds on proof length in proof systems for quantified Boolean formulas. A key notion in this framework is that of proof system ensemble, which is (essentially) a sequence of proof systems where, for each, proof checking can be performed in the polynomial hierarchy. We introduce a proof system ensemble called relaxing QU-res that is based on the established proof system QU-resolution. Our main results include an exponential separation of the treelike and general versions of relaxing QU-res and an exponential lower bound for relaxing QU-res; these are analogs of classical results in propositional proof complexity.
Metadata
| Item Type: | Article |
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| Additional Information: | © ACM, 2017. This is the author's version of the work. It is posted here by permission of ACM for your personal use. Not for redistribution. The definitive version was published at the link above. |
| School: | Birkbeck Faculties and Schools > Faculty of Science > School of Computing and Mathematical Sciences |
| Depositing User: | Hubie Chen |
| Date Deposited: | 18 Apr 2018 12:30 |
| Last Modified: | 09 Aug 2023 12:43 |
| URI: | https://eprints.bbk.ac.uk/id/eprint/21942 |
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