Multi-linearity self-testing with relative error

Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)

Volumn 1770, Issue , 2000, Pages 302-313

  Magniez, Frédéric ^a  

^a UNIVERSITÉ PARIS SACLAY   (France)

Author keywords

Approximation error; Program verification; Robustness and stability of functional equations; Self testing programs

Indexed keywords

RATIONAL FUNCTIONS; SOFTWARE TESTING; TESTING;

APPROXIMATION ERRORS; MULTILINEAR FUNCTIONS; NUMERICAL COMPUTATIONS; PROGRAM VERIFICATION; RELATIVE ERRORS; ROBUSTNESS AND STABILITY OF FUNCTIONAL EQUATIONS; SELF-TESTING PROGRAMS; SIMPLE OPERATION;

ERRORS;

EID: 33645261950     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-46541-3_25     Document Type: Conference Paper

References (22)

1. S. Ar, M. Blum, B. Codenotti, and P. Gemmell. Checking approximate computations over the reals. In Proc. 25th STOC, pages 786-795, 1993.
2. S. Arora, C. Lund, R. Motwani, M. Sudan, and M. Szegedy. Proof verification and intractibility of approximation problems. In Proc. 33rd FOCS, pages 14-23, 1992.
3. S. Arora and S. Safra. Probabilistic checkable proofs: A new characterization of NP. In Proc. 33rd FOCS, pages 1-13, 1992.
4. L. Babai. Transparent (holographic) proofs. In Proc. 10th STACS, volume 665, pages 525-534. LNCS, 1993.
5. M. Blum and S. Kannan. Designing programs that check their work. J. ACM, 42(1):269-291, 1995.
6. M. Blum, M. Luby, and R. Rubinfeld. Self-testing/correcting with applications to numerical problems. J. Comp. and Syst. Sci., pages 549-595, 1993.
7. M. Blum. Designing programs to check their work. Technical Report 88-009, ICSI, 1988.
8. D. Coppersmith, December 1989. See discussion in [BLR93].
9. F. Ergün, S. Ravi Kumar, and R. Rubinfeld. Approximate checking of polynomials and functional equations. In Proc. 37th FOCS, pages 592-601, 1996.
10. K. Friedl, Z. Hátsági, and A. Shen. Low-degree tests. Proc. 5th SODA, pages 57-64, 1994.
11. G. L. Forti. Hyers-Ulam stability of functional equations in several variables. Aeq. Mathematicae, 50:143-190, 1995.
12. O. Goldreich, S. Goldwasser, and D. Ron. Property testing and its connection to learning and approximation. In Proc. 37th FOCS, pages 339-348, 1996.
13. P. Gemmell, R. Lipton, R. Rubinfeld, M. Sudan, and A. Wigderson. Selftesting/ correcting for polynomials and for approximate functions. In Proc. 23rd STOC, pages 32-42, 1991.
14. O. Goldreich and D. Ron. Property testing in bounded degree graphs. In Proc. 37th STOC, pages 406-415, 1997.
15. D. H. Hyers and T. M. Rassias. Approximate homomorphisms. Aeq. Mathematicae, 44:125-153, 1992.
16. D. H. Hyers and P. Šemrl. On the behaviour of mappings which do not satisfy Hyers-Ulam stability. Proc. AMS, 144(4):989-993, April 1992.
17. D. H. Hyers. On the stability of the linear functional equation. Proc. Nat. Acad. Sci., U.S.A., 27:222-224, 1941.
18. M. Kiwi, F. Magniez, and M. Santha. Approximate testing with relative error. In Proc. 31st STOC, pages 51-60, 1999.
19. R. Lipton. New directions in testing. Series in Discrete Mathematics and Theoretical Computer Science, 2:191-202, 1991.
20. R. Rubinfeld and M. Sudan. Robust characterizations of polynomials with applications to program testing. SIAM J. Comp., 25(2):23-32, April 1996.
21. R. Rubinfeld. On the robustness of functional equations. SIAM J. Comp., 28(6):1972-1997, 1999.
22. F. Skof. Sull’approssimazione delle applicazioni localmente δ-additive. Atti Acc. Sci. Torino, 117:377-389, 1983. in Italian.