Chinese remaindering with errors
STOC '99 Proceedings of the thirty-first annual ACM symposium on Theory of computing
Modern computer algebra
The Byzantine Generals Problem
ACM Transactions on Programming Languages and Systems (TOPLAS)
Byzantine generals in action: implementing fail-stop processors
ACM Transactions on Computer Systems (TOCS)
An output-sensitive variant of the baby steps/giant steps determinant algorithm
Proceedings of the 2002 international symposium on Symbolic and algebraic computation
"Soft-decision" decoding of Chinese remainder codes
FOCS '00 Proceedings of the 41st Annual Symposium on Foundations of Computer Science
Efficient computation of the characteristic polynomial
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
Proceedings of the 2007 international workshop on Parallel symbolic computation
Algorithm-Based Fault Tolerance for Matrix Operations
IEEE Transactions on Computers
Processor-Oblivious Parallel Stream Computations
PDP '08 Proceedings of the 16th Euromicro Conference on Parallel, Distributed and Network-Based Processing (PDP 2008)
Algorithm-based fault tolerance applied to high performance computing
Journal of Parallel and Distributed Computing
Proceedings of the 37th International Symposium on Symbolic and Algebraic Computation
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We study algorithm based fault tolerance techniques for supporting malicious errors in distributed computations based on Chinese remainder theorem. The description holds for both computations with integers or with polynomials over a field. It unifies the approaches of redundant residue number systems and redundant polynomial systems through the Reed Solomon decoding algorithm proposed by Gao. We propose several variations on the application of the extended Euclid algorithm, where the error correction rate is adaptive. Several improvements are studied, including the use of various criterions for the termination of the Euclidean Algorithm, and an acceleration using the Half-GCD techniques. When there is some redundancy in the input, a gap in the quotient sequence is stated at the step matching the error correction, which enables early termination parallel computations. Experiments are shown to compare these approaches.