Abstract
Assuming random computational errors in the execution of a RAM program, we discuss how to obtain a correct result with a given confidence bound. An algorithm ALG (requiring A operations) is used in connection with a certificate CERT (requiring C operations, C≤A). CERT assesses the result of ALG, however, it may fail as well. Each operation of ALG (resp. CERT) is repeated k (resp. h) times, and the result of the operation is established by majority voting. Letting π be the success probability of an operation, and 1−δ be the desired confidence on the overall result, k and h are evaluated as functions of A, C,-π and δ. The resulting running time is reduced by a factor of up to A/C over the time required without using CERT, for the same value of δ.
Two case studies with C<A are examined, their expected behavior is analyzed, and computational results on the running times are presented.
Supported in part by MURST of Italy.
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References
A. Aho, Hopcroft, Ullman, The Design and Analysis of Computer Algorithms, Addison-Wesley, Reading, MA, 1974.
M. Blum and S. Kannan, Designing programs that check their work, Proc. 21st ACM Symposium on the Theory of Computing (1989), 86–95.
M. Blum, M. Luby, and R. Rubinfeld, Self-testing and self-correction programs with applications to numerical problems, Proc. 22nd ACM Symposium on the Theory of Computing (1990), 73–83.
M. Blum, W. Evans, P. Gemmell, S. Kannan, and M. Naor, Checking the correctness of memories, Proc. IEEE Symposium on the Foundations of Computer Science (1991), 90–99.
R.S. Borgstrom and S.R. Kosaraju, Comparison-based search in the presence of errors, Proc. 25th ACM Symposium on the Theory of Computing (1993), 130–136.
U. Feige, P. Raghavan, D. Peleg, and E. Upfal, Computing with noisy information, SIAM Journal on Computing, 23 (1994), 1001–1018.
D.E. Knuth, The Art of Computer Programming, vol. 3: Sorting and Searching, Addison-Wesley, Reading, MA, 1973.
K.B. Lakshmanan, B. Ravikumar, and K. Ganesan, Coping with erroneous information while sorting, IEEE Transactions on Computers, 40 (1991), 1081–1084.
F. Luccio and A. Pedrotti, Combinatorial algorithms in the presence of random errors, Dipartimento di Informatica, University of Pisa, Technical Report TR-13/95 (1995).
N. Pippenger, Analysis of error correction by majority voting, in Advances in Computing Research, Volume 5, JAI Press, 1989, pp. 171–198.
N. Pippenger, Reliable computation by formulas in the presence of noise. IEEE Transactions on Information Theory, 34 (1988), 194–197.
N. Pippenger, On networks of noisy gates, Proc. IEEE Symposium on the Foundations of Computer Science (1985), 30–38.
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© 1997 Springer-Verlag Berlin Heidelberg
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Luccio, F., Pedrotti, A. (1997). Design of reliable combinatorial algorithms using certificates. In: Bongiovanni, G., Bovet, D.P., Di Battista, G. (eds) Algorithms and Complexity. CIAC 1997. Lecture Notes in Computer Science, vol 1203. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-62592-5_68
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DOI: https://doi.org/10.1007/3-540-62592-5_68
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