Information Processing Letters
Reductions in circuit complexity: an isomorphism theorem and a gap theorem
Journal of Computer and System Sciences - Eleventh annual conference on structure and complexity 1996
Reducing the complexity of reductions
Computational Complexity
Introduction to Circuit Complexity: A Uniform Approach
Introduction to Circuit Complexity: A Uniform Approach
On Pseudorandom Generators in NC
MFCS '01 Proceedings of the 26th International Symposium on Mathematical Foundations of Computer Science
Random Structures & Algorithms
Verifying and decoding in constant depth
Proceedings of the thirty-ninth annual ACM symposium on Theory of computing
SIAM Journal on Computing
On Pseudorandom Generators with Linear Stretch in NC0
Computational Complexity
Planar and Grid Graph Reachability Problems
Theory of Computing Systems - Special Issue: Computation and Logic in the Real World; Guest Editors: S. Barry Cooper, Elvira Mayordomo and Andrea Sorbi
Cryptography with Constant Input Locality
Journal of Cryptology
A tight Karp-Lipton collapse result in bounded arithmetic
ACM Transactions on Computational Logic (TOCL)
The isomorphism conjecture for constant depth reductions
Journal of Computer and System Sciences
Proof systems that take advice
Information and Computation
Verifying proofs in constant depth
MFCS'11 Proceedings of the 36th international conference on Mathematical foundations of computer science
Extractors for Circuit Sources
FOCS '11 Proceedings of the 2011 IEEE 52nd Annual Symposium on Foundations of Computer Science
One-input-face MPCVP is hard for l, but in LogDCFL
FSTTCS'06 Proceedings of the 26th international conference on Foundations of Software Technology and Theoretical Computer Science
Optimal acceptors and optimal proof systems
TAMC'10 Proceedings of the 7th annual conference on Theory and Applications of Models of Computation
The Complexity of Distributions
SIAM Journal on Computing
Hi-index | 0.00 |
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.