3,021 research outputs found
Deterministic voting in distributed systems using error-correcting codes
Distributed voting is an important problem in reliable computing. In an N Modular Redundant (NMR) system, the N computational modules execute identical tasks and they need to periodically vote on their current states. In this paper, we propose a deterministic majority voting algorithm for NMR systems. Our voting algorithm uses error-correcting codes to drastically reduce the average case communication complexity. In particular, we show that the efficiency of our voting algorithm can be improved by choosing the parameters of the error-correcting code to match the probability of the computational faults. For example, consider an NMR system with 31 modules, each with a state of m bits, where each module has an independent computational error probability of 10^-3. In, this NMR system, our algorithm can reduce the average case communication complexity to approximately 1.0825 m compared with the communication complexity of 31 m of the naive algorithm in which every module broadcasts its local result to all other modules. We have also implemented the voting algorithm over a network of workstations. The experimental performance results match well the theoretical predictions
Deterministic Voting in Distributed Systems Using Error-Correcting Codes
Distributed voting is an important problem in reliable computing. In an N
Modular Redundant (NMR) system, the N computational modules execute identical tasks
and they need to periodically vote on their current states. In this paper, we propose a
deterministic majority voting algorithm for NMR systems. Our voting algorithm uses
error-correcting codes to drastically reduce the average case communication
complexity. In particular, we show that the efficiency of our voting algorithm can be improved
by choosing the parameters of the error correcting code to match the probability of
the computational faults. For example, consider an NMR system with 31 modules,
each with a state of m bits, where each module has an independent computational
error probability of 10 to the power of minus 3. In this NMR system, our algorithm can reduce the average case communication complexity to approximately 1.0825m compared with the
communication complexity of 31m of the naive algorithm in which every module broadcasts
its local result to all other modules. We have also implemented the voting algorithm
over a network of workstations. The experimental performance results match well the
theoretical predictions
Standard interface definition for avionics data bus systems
Data bus for avionics system of space shuttle, noting functions of interface unit, error detection and recovery, redundancy, and bus control philosoph
Three Puzzles on Mathematics, Computation, and Games
In this lecture I will talk about three mathematical puzzles involving
mathematics and computation that have preoccupied me over the years. The first
puzzle is to understand the amazing success of the simplex algorithm for linear
programming. The second puzzle is about errors made when votes are counted
during elections. The third puzzle is: are quantum computers possible?Comment: ICM 2018 plenary lecture, Rio de Janeiro, 36 pages, 7 Figure
Solving Multiclass Learning Problems via Error-Correcting Output Codes
Multiclass learning problems involve finding a definition for an unknown
function f(x) whose range is a discrete set containing k > 2 values (i.e., k
``classes''). The definition is acquired by studying collections of training
examples of the form [x_i, f (x_i)]. Existing approaches to multiclass learning
problems include direct application of multiclass algorithms such as the
decision-tree algorithms C4.5 and CART, application of binary concept learning
algorithms to learn individual binary functions for each of the k classes, and
application of binary concept learning algorithms with distributed output
representations. This paper compares these three approaches to a new technique
in which error-correcting codes are employed as a distributed output
representation. We show that these output representations improve the
generalization performance of both C4.5 and backpropagation on a wide range of
multiclass learning tasks. We also demonstrate that this approach is robust
with respect to changes in the size of the training sample, the assignment of
distributed representations to particular classes, and the application of
overfitting avoidance techniques such as decision-tree pruning. Finally, we
show that---like the other methods---the error-correcting code technique can
provide reliable class probability estimates. Taken together, these results
demonstrate that error-correcting output codes provide a general-purpose method
for improving the performance of inductive learning programs on multiclass
problems.Comment: See http://www.jair.org/ for any accompanying file
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