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 present a general construction of proof systems for regular languages with strongly connected NFA's. © 2011 Springer-Verlag GmbH.
Cite
CITATION STYLE
Beyersdorff, O., Datta, S., Mahajan, M., Scharfenberger-Fabian, G., Sreenivasaiah, K., Thomas, M., & Vollmer, H. (2011). Verifying proofs in constant depth. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 6907 LNCS, pp. 84–95). https://doi.org/10.1007/978-3-642-22993-0_11
Register to see more suggestions
Mendeley helps you to discover research relevant for your work.
