Designing programs that check their work
STOC '89 Proceedings of the twenty-first annual ACM symposium on Theory of computing
Self-testing/correcting for polynomials and for approximate functions
STOC '91 Proceedings of the twenty-third annual ACM symposium on Theory of computing
A mathematical theory of self-checking, self-testing and self-correcting programs
A mathematical theory of self-checking, self-testing and self-correcting programs
Self-testing polynomial functions efficiently and over rational domains
SODA '92 Proceedings of the third annual ACM-SIAM symposium on Discrete algorithms
Checking approximate computations over the reals
STOC '93 Proceedings of the twenty-fifth annual ACM symposium on Theory of computing
Self-testing/correcting with applications to numerical problems
Journal of Computer and System Sciences - Special issue: papers from the 22nd ACM symposium on the theory of computing, May 14–16, 1990
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
The art of computer programming, volume 2 (3rd ed.): seminumerical algorithms
On the Robustness of Functional Equations
SIAM Journal on Computing
Robust Characterizations of Polynomials withApplications to Program Testing
SIAM Journal on Computing
Hiding Instances in Multioracle Queries
STACS '90 Proceedings of the 7th Annual Symposium on Theoretical Aspects of Computer Science
Approximate checking of polynomials and functional equations
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
Property testing and its connection to learning and approximation
FOCS '96 Proceedings of the 37th Annual Symposium on Foundations of Computer Science
SIAM Journal on Discrete Mathematics
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We formalize the notion and initiate the investigation of approximate testing for arbitrary forms of the error term. Until now only the case of absolute error had been addressed ignoring the fact that often only the most significant figures of a numerical calculation are valid. This work considers approximation errors whose magnitude grows with the size of the input to the program. We demonstrate the viability of this new concept by addressing the basic and benchmark problem of self-testing for the class of linear and polynomial functions. We obtain stronger versions of results of Ergün et al. (Proceedings of the 37th FOCS, 1996, pp. 592-601) by exploiting elegant techniques from Hyers-Ulam stability theory.