R. Rubinfeld and M. Sudan, Testing polynomial functions eciently and over rational domains, Proceedings of the 3 Annual ACM-SIAM Symposium on Discrete Algorithms (1992), 23-43.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....the scope of a testing survey. The rst result regarding testability per se is probably that of Blum, Luby and Rubinfeld [13] concerning linearity, and the rst explicit de nition of property testing was given by Rubinfeld and Sudan in [43] in its turn it is based on some of the results of [44] and [26] The rst results dealt mainly with the algebraic notion of being a low degree polynomial. Suppose that for some nite eld F the input is given as a function f from F to F , that queries consist of nding the value of f at a speci ed location x 2 F , and that the distance is measured ....

R. Rubinfeld and M. Sudan, Testing polynomial functions eciently and over rational domains, Proceedings of the 3 Annual ACM-SIAM Symposium on Discrete Algorithms (1992), 23-43.

....P that is correct on most inputs and uses it to compute f correctly on every input with high probability. The program checker, self tester and self corrector may call the program This paper uni es and extends part of the results contained in Gemmell et al. GLRSW91] and Rubinfeld and Sudan [RS92]. y Cornell University. email: ronitt cs.cornell.edu. This work is supported by ONR Young Investigator grant N00014 93 1 0590 and the United States Israel Binational Science Foundation grant 92 00226. Part of this work was done while the author was at Princeton University, supported by DIMACS ....

.... results focus on tests that are close variants of the test given in [BFL91] The low degree test given here is fundamentally di erent from the ones mentioned above and originated from independent considerations in the work of [GLRSW91] The eciency of the tester shown here may also be found in [RS92]. It turns out that this tester is particularly well suited to such multiple prover applications and provides a one round, constant prover proof that a function is a low degree polynomial over nite elds. This is observed in subsequent work of [ALMSS92] see also [Sud92] and follows by using an ....

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R. Rubinfeld and M. Sudan. Testing polynomial functions eciently and over rational domains. In Proceedings of the 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 23-43, 1992.

....of programs that we deal with are those computing polynomials and functions de ned by certain types of functional equations. We present results showing how to perform approximate checking, self testing, and self correcting of polynomials, settling in the armative a question raised by [GLR 91, RS92, RS96] We obtain this by rst building approximate self testers for linear and multilinear functions. We then This work is partially supported by NSF Career grant CCR 9624552, the Alfred P. Sloan Research Award, and ONR grant N00014 97 1 0505. The rst and second authors are also supported ....

....by the method of successive di erences which never explicitly interpolates the polynomial computed by the program, thus giving a particularly simple and ecient (O(d 2 ) operations) test. We can show that the interpolation identity is approximately robust by modifying the robustness theorem in [RS92] Section 3.3) Our proof of stability of the interpolation identity (Section 3.2) however, uses a characterization of polynomials in terms of multilinear functions that previously has not been applied to program checking. This in turn allows us to use our results on the stability of ....

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R. Rubinfeld and M. Sudan. Testing polynomial functions eciently and over rational domains. Proc. 3rd ACM Symposium on Discrete Algorithms, pp. 23-43, 1992.

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