Beyersdorff, O, Datta, S, Krebs, A et al. (5 more authors) (2013) Verifying proofs in constant depth. ACM Transactions on Computation Theory (TOCT), 5 (1). 2. ISSN 1942-3454
Abstract
In this paper we initiate the study of proof systems where verification of proofs proceeds by NC0 circuits. We investigate the question which languages admit proof systems in this very restricted model. Formulated alternatively, we ask which languages can be enumerated by NC0 functions. Our results show that the answer to this problem is not determined by the complexity of the language. On the one hand, we construct NC0 proof systems for a variety of languages ranging from regular to NP complete. On the other hand, we show by combinatorial methods that even easy regular languages such as Exact-OR do not admit NC0 proof systems. We also show that Majority does not admit NC0 proof systems. Finally, we present a general construction of NC0 proof systems for regular languages with strongly connected NFA's.
Metadata
Item Type: | Article |
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Authors/Creators: |
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Copyright, Publisher and Additional Information: | © ACM, 2013. 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 in ACM Transactions on Computation Theory (TOCT), 5, 1, 2, 2013, http://doi.acm.org/10.1145/2462896.2462898 |
Keywords: | Circuit complexity; proof circuits; proof complexity; small depth proofs |
Dates: |
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Institution: | The University of Leeds |
Academic Units: | The University of Leeds > Faculty of Engineering & Physical Sciences (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds) |
Depositing User: | Symplectic Publications |
Date Deposited: | 23 Jun 2014 11:27 |
Last Modified: | 25 Jun 2014 09:54 |
Published Version: | http://dx.doi.org/10.1145/2462896.2462898 |
Status: | Published |
Publisher: | Elsevier |
Identification Number: | 10.1145/2462896.2462898 |
Open Archives Initiative ID (OAI ID): | oai:eprints.whiterose.ac.uk:79314 |