Beyersdorff, O, Vollmer, H, Datta, S, Mahajan, M, Sreenivasaiah, K, Scharfenberger-Fabian, G and Thomas, M (2011) Verifying proofs in constant depth. In: Proceedings MFCS 2011. Mathematical Foundations of Computer Science 2011, 22 - 26 August 2011, Warsaw, Poland. Springer Verlag , 84 - 95 . ISBN 978-3-642-22992-3
In this paper we initiate the study of proof systems where verification of proofs proceeds by NC 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 NC 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 NC 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 NC proof systems. We also present a general construction of proof systems for regular languages with strongly connected NFA's.
|Copyright, Publisher and Additional Information:||(c) 2011, Springer Verlag. This is an author produced version of a paper published in Proceedings MFCS 2011. Uploaded in accordance with the publisher's self-archiving policy. The original publication is available at www.springerlink.com.|
|Institution:||The University of Leeds|
|Academic Units:||The University of Leeds > Faculty of Engineering (Leeds) > School of Computing (Leeds) > Institute for Computational and Systems Science (Leeds)|
|Depositing User:||Symplectic Publications|
|Date Deposited:||06 Dec 2012 16:35|
|Last Modified:||18 Sep 2016 18:22|