Optimal parallel selection had complexity O(log log N)
Journal of Computer and System Sciences - 18th Annual ACM Symposium on Theory of Computing (STOC), May 28-30, 1986
Reliable computation with noisy circuits and decision trees—a general n log n lower bound
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
On the complexity of finite random functions
Information Processing Letters
Computing with Noisy Information
SIAM Journal on Computing
Fault-tolerant quantum computation with constant error
STOC '97 Proceedings of the twenty-ninth annual ACM symposium on Theory of computing
On the design of reliable Boolean circuits that contain partially unreliable gates
Journal of Computer and System Sciences
Average-Case Lower Bounds for Noisy Boolean Decision Trees
SIAM Journal on Computing
Computation in noisy radio networks
Proceedings of the ninth annual ACM-SIAM symposium on Discrete algorithms
Tight Bounds on the Size of Fault-Tolerant Merging and Sorting Networks with Destructive Faults
SIAM Journal on Computing
Finding OR in a noisy broadcast network
Information Processing Letters
The invasiveness of off-line memory checking
STOC '02 Proceedings of the thiry-fourth annual ACM symposium on Theory of computing
Searching games with errors---fifty years of coping with liars
Theoretical Computer Science
Computing Boolean Functions from Multiple Faulty Copies of Input Bits
LATIN '02 Proceedings of the 5th Latin American Symposium on Theoretical Informatics
Boosting in the presence of noise
Proceedings of the thirty-fifth annual ACM symposium on Theory of computing
Reliable cellular automata with self-organization
FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
Highly fault-tolerant parallel computation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Computing in Fault Tolerance Broadcast Networks
CCC '04 Proceedings of the 19th IEEE Annual Conference on Computational Complexity
Coding for interactive communication
IEEE Transactions on Information Theory - Part 1
On the maximum tolerable noise for reliable computation by formulas
IEEE Transactions on Information Theory
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We show that a noisy parallel decision tree making O(n) queries needs Ω(log* n) rounds to compute OR of n bits. This answers a question of Newman [21]. We prove more general trade-offs between the number of queries and rounds. We also completely settle a similar question for computing MAX in the noisy comparison tree model; these results bring out interesting differences among the noise models.