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Proceedings of 37th Conference on Foundations of Computer Science (1996)
Burlington, VT
Oct. 14, 1996 to Oct. 16, 1996
ISBN: 0-8186-7594-2
pp: 592
F. Ergun , Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
S.R. Kumar , Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
R. Rubinfeld , Dept. of Comput. Sci., Cornell Univ., Ithaca, NY, USA
ABSTRACT
The authors show how to check programs that compute polynomials and functions defined by addition theorems-in the realistic setting where the output of the program is approximate instead of exact. They present results showing how to perform approximate checking, self-testing, and self-correcting of polynomials, settling in the affirmative a question raised by Gemmell et al. (1991), and Rubinfeld and Sudan (1992, 1996). They then show how to perform approximate checking, self-testing, and self-correcting for those functions that satisfy addition theorems, settling a question raised by Rubinfeld (1994]) In both cases, they show that the properties used to test programs for these functions are both robust (in the approximate sense) and stable. Finally, they explore the use of reductions between functional equations in the context of approximate self-testing. Their results have implications to the stability theory of functional equations.
INDEX TERMS
polynomials; program checking; approximate checking; polynomial computation; functional equation computation; functions; addition theorems; approximate program output; self-testing; self-correcting; program testing; reductions; stability theory
CITATION

R. Rubinfeld, F. Ergun and S. Kumar, "Approximate checking of polynomials and functional equations," Proceedings of 37th Conference on Foundations of Computer Science(FOCS), Burlington, VT, 1996, pp. 592.
doi:10.1109/SFCS.1996.548518
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