Rounds vs queries trade-off in noisy computation
SODA '05 Proceedings of the sixteenth annual ACM-SIAM symposium on Discrete algorithms
Lower Bounds for the Noisy Broadcast Problem
FOCS '05 Proceedings of the 46th Annual IEEE Symposium on Foundations of Computer Science
A tight lower bound for parity in noisy communication networks
Proceedings of the nineteenth annual ACM-SIAM symposium on Discrete algorithms
Towards efficient designs for in-network computing with noisy wireless channels
INFOCOM'10 Proceedings of the 29th conference on Information communications
Making polynomials robust to noise
STOC '12 Proceedings of the forty-fourth annual ACM symposium on Theory of computing
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We consider a fault tolerance broadcast network of nprocessors each holding one bit of information. The goal isto compute a given Boolean function on the n bits. In eachstep, a processor may broadcast one bit of information.Each listening processor receives the bit that was broadcastedwith error probability bounded by a fixed constant \varepsilon.The errors in different steps, as well as for different receivingprocessors in the same step, are mutually independent.The protocols that are considered in this model are obliviousprotocols: At each step, the processors that broadcastare fixed in advanced and independent of the input and theoutcome of previous steps. The primal complexity measurein this model is the total number of broadcasts that is performedby the protocol.We present here the first linear complexity protocolsfor several classes of Boolean functions, including the ORfunction, functions that have 0(1)-minterm (maxterm) size,functions that have linear size AC_0 formulae and someother functions. This answer an open question of Yao [22],considering this fault tolerance model of El Gamal [2] andGallager [8].