How to generate cryptographically strong sequences of pseudo-random bits
SIAM Journal on Computing
Random oracles separate PSPACE from the polynomial-time hierarchy
Information Processing Letters
On hiding information form an oracle
Journal of Computer and System Sciences
Algebraic methods for interactive proof systems
Journal of the ACM (JACM)
Journal of the ACM (JACM)
On the power of two-local random reductions
Information Processing Letters
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
Designing programs that check their work
Journal of the ACM (JACM)
Interactive proofs and the hardness of approximating cliques
Journal of the ACM (JACM)
Probabilistic checking of proofs: a new characterization of NP
Journal of the ACM (JACM)
Proof verification and the hardness of approximation problems
Journal of the ACM (JACM)
Quantum computation and quantum information
Quantum computation and quantum information
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Optimal Lower Bounds for Quantum Automata and Random Access Codes
FOCS '99 Proceedings of the 40th Annual Symposium on Foundations of Computer Science
A Lattice Problem in Quantum NP
FOCS '03 Proceedings of the 44th Annual IEEE Symposium on Foundations of Computer Science
Limitations of Quantum Advice and One-Way Communication
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Exponential lower bound for 2-query locally decodable codes via a quantum argument
Journal of Computer and System Sciences - Special issue: STOC 2003
The Quantum Adversary Method and Classical Formula Size Lower Bounds
CCC '05 Proceedings of the 20th Annual IEEE Conference on Computational Complexity
Journal of the ACM (JACM)
Lower Bounds for Local Search by Quantum Arguments
SIAM Journal on Computing
A tight lower bound for restricted PIR protocols
Computational Complexity
2-Local Random Reductions to 3-Valued Functions
Computational Complexity
Improved lower bounds for locally decodable codes and private information retrieval
ICALP'05 Proceedings of the 32nd international conference on Automata, Languages and Programming
Lower bounds on matrix rigidity via a quantum argument
ICALP'06 Proceedings of the 33rd international conference on Automata, Languages and Programming - Volume Part I
Hi-index | 0.00 |
We use a quantum computational argument to prove, for any integer k ≥ 2, a complexity upper bound for nonadaptive k-query classical locally random reductions (LRRs) that allow bounded-errors. Extending and improving a recent result of Pavan and Vinodchandran [PV], we prove that if a set L has a nonadaptive 2-query classical LRR to functions g and h, where both g and h can output O(log n) bits, such that the reduction succeeds with probability at least 1/2 + 1/poly(n), then L ∈ PPNP/poly. Previous complexity upper bound for nonadaptive 2-query classical LRRs was known only for much restricted LRRs: LRRs in which the target functions can only take values in {0, 1, 2} and the error probability is zero [PV]. For k 2, we prove that if a set L has a nonadaptive k-query classical LRR to boolean functions g1, g2, ..., gk such that the reduction succeeds with probability at least 2/3 and the distribution on (k/2+ √k)-element subsets of queries depends only on the input length, then L ∈ PPNP/poly. Previously, for no constant k 2, a complexity upper bound for nonadaptive k-query classical LRRs was known even for LRRs that do not make errors. Our proofs follow a two stage argument: (1) simulate a nonadaptive k-query classical LRR by a 1-query quantum weak LRR, and (2) upper bound the complexity of this quantum weak LRR. To carry out the two stages, we formally define nonadaptive quantum weak LRRs, and prove that if a set L has a 1-query quantum weak LRR to a function g, where g can output polynomial number of bits, such that the reduction succeeds with probability at least 1/2 + 1/poly(n), then L ∈ PPNP/poly.