Abstract
Suppose P is a program designed to compute a linear function f on a group G. The task of self-testing f, that is, testing if P computes f correctly on most inputs, usually involves checking if P computes f correctly on all the generators of G. Recently, F. Ergün presented self-testers that avoid this generator bottleneck for specific functions. In this paper, we generalize Ergün's results, and extend them to a much larger class of functions. Our results give efficient self-testers for polynomial differentiation, integration, arithmetic in large finite field extensions, and constant-degree polynomials over large rings.
Research supported in part by ONR Young Investigator Award N00014-93-1-0590.
Research supported in part by NSF grant CCR-9409104.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
References
L. Babai, L. Fortnow, and C. Lund. Non-deterministic exponential time has two-prover interactive protocols. Computational Complexity, 1:3–40, 1991.
M. Blum and S. Kannan. Designing programs that check their work. In Proc. 21st Annual ACM Symposium on the Theory of Computing, pages 86–97, 1989.
M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. J. Comp. Sys. Sci., 47(3):549–595, 1993. An earlier version appeared in STOC 1990.
M. Blum and H. Wasserman. Program result-checking: A theory of testing meets a test of theory. In Proc. 35 th Annual IEEE Symposium on Foundations of Computer Science, pages 382–392, 1994.
F. Ergün. Testing multivariate linear functions: Overcoming the generator bottleneck. In Proc. 27th Annual ACM Symposium on the Theory of Computing, pages 407–416, 1995.
U. Feige, S. Goldwasser, L. Lovasz, S. Safra, and M. Szegedy. Approximating clique is almost NP-complete. In Proc. 32nd Annual IEEE Symposium on Foundations of Computer Science, pages 2–12, 1991.
P. Gemmell, R. Lipton, R. Rubinfeld, M. Sudan, and A. Wigderson. Self-testing/ correcting for polynomials and for approximate functions. In Proc. 23rd Annual ACM Symposium on the Theory of Computing, pages 32–42, 1991.
R. Lipton. New directions in testing. In Proc. of DIMACS Workshop on Distributed Computingand Cryptography, pages 191–202, 1991.
R. Rubinfeld and M. Sudan. Testing polynomial functions efficiently and over rational domains. In Proc. 3rd Annual ACM-SIAM Symposium on Discrete Algorithms, pages 23–43, 1992.
R. Rubinfeld and M. Sudan. Robust characterizations of polynomials and their applications to program testing. TR 93-1387, Dept. of Computer Science, Cornell University, 1993. To appear in SIAM Journal of Computing.
R. Rubinfeld. A Mathematical Theory of Self-Checking, Self-Testing, and Self-Correcting Programs. PhD thesis, University of California at Berkeley, 1990.
R. Rubinfeld. Robust functional equations with applications to self-testing/ correcting. In Proc. 35th Annual IEEE Symposium on Foundations of Computer Science, pages 288–299, 1994.
Madhu Sudan. On the role of algebra in the efficient verification of proofs. In M. Agrawal, V. Arvind, and M. Mahajan, editors, Proc. Workshop on Algebraic Methods in Complexity Theory (AMCOT), pages 58–68, 1994. Technical Report IMSc 94/51, The Institute of Mathematical Sciences, Madras, India.
Author information
Authors and Affiliations
Editor information
Rights and permissions
Copyright information
© 1995 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
Ravikumar, S., Sivakumar, D. (1995). On self-testing without the generator bottleneck. In: Thiagarajan, P.S. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1995. Lecture Notes in Computer Science, vol 1026. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-60692-0_53
Download citation
DOI: https://doi.org/10.1007/3-540-60692-0_53
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-60692-5
Online ISBN: 978-3-540-49263-4
eBook Packages: Springer Book Archive