M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. Journal of Computer and System Sciences, 47:549--595, 1993.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....step [MNS 96, KW98] A general formulation structural filtering is proposed in [FMN99] Probabilistic analysis [DP99] shows the e#cacy of arithmetic filters. The filtering of determinants is treated in several papers [Cla92, BBP01, PY01, BY00] Filtering is related to program checking [BK95, BLR93] View a computational problem P as an input output relation, P I O where I , O is the input and output spaces respectively. Let be A a (standard) algorithm for P which, viewed as a total function A : I # NaN , has the property that for all i I , i, A(i) P i# there is some o ....

M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. J. of Computer and System Sciences, 47:549--595, 1993.

....types of problems, Rubinfeld and Sudan [RS96] and Goldreich, Goldwasser and Ron [GGR98] have developed the notion of property testing. Testable properties come in many varieties including graph properties (e.g. GGR98, AFKS99, Fis01a, Fis01b, Alo01, GT01] algebraic properties of functions [BLR93, RS96, EKK 00] and regular languages [ANKS99] Ron [Ron00] gives a nice survey of this area. In this model, the property tester has random access to the n input bits similar to the black box oracle model. The tester can query only a small, usually some xed constant, probabilistically chosen ....

M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. Journal of Computer and System Sciences, 47:549{ 595, 1993.

....Prover P Figure 2: Probabilistically Checkable Proofs PCP (q; r) denotes the class of languages with probabilistically checkable proofs using parameters q and r. A substantial, but rapid series of advances in interactive proof systems [BM88, GMR89, LFKN90, BFL91] self testing programs [BK89, BLR90] and derandomization [CW89, IZ89] lead to the central theorem of Arora, et al. ALM 92] Theorem 2 ( ALM 92] NP = PCP (logn; 1) This theorem states that for any NP language a probabilistic, polynomial time algorithm exists which can verify purported proofs of membership in that ....

M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. In Proc. 22th ACM Symp. on the Theory of Computing. ACM, 1990.

....other s stories without communicating. We shall see later in this paper that this sort of corroboration is the key to the additional power of multiple provers. Interactive proof systems have seen a number of important applications to cryptography [23, 22] algebraic complexity [3] program testing [7, 8] and distributed computation [16, 23] For example, a chain of results concerning interactive proof systems [22, 3, 24, 9] conclude that if the graph isomorphism problem is NP complete then the polynomial time hierarchy collapses. Multiple prover interactive proof systems have also seen several ....

M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. In Proceedings of the 22nd ACM Symposium on the Theory of Computing, pages 73--83. ACM, New York, 1990.

....the course of the proof of the main theorem, we show how to test whether a function in several variables over Z, given as an oracle, is multilinear over a large interval. This test has independent interest for program testing and correction, in the context of Blum Kannan [12] Blum Luby Rubinfeld [13], and Lipton [28] see Section 6) The reduction to the test involves ideas of the PSPACE = IP proof (arithmetic extrapolation of truth values) The proof of correctness of the multilinearity test rests on combinatorial techniques. A more efficient multilinearity test, with important consequences, ....

....checkers. This is directly related to the question of whether coNP languages have protocols with NP provers (see Section 4.6) 6.3. Self Testing and Self Correcting Programs. Our test of multilinear functions (Section 5) also has applications to program testing as described by Blum Luby Rubinfeld [13] and Lipton [28] We will use the following definition of self testing correcting programs slightly different from but in the spirit of the Blum Luby Rubinfeld definition. We make the connection between the two models clear in Section 6.4. An input set I is a sequence of subsets I 1 ; I 2 ; ....

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M. Blum, M. Luby, and R. Rubinfeld, Self-testing and self-correcting programs, with applications to numerical programs, in Proc. 22nd Ann. ACM Symp. Theory of Computing, 1990, 73-83.

....PRAB s mod 2. A simplified proof of Toda s Theorem PH P ]P follows. As a further consequence, we show that ] mP has interactive proofs with ] mP powerful honest provers, thus exhibiting an infinite class of natural and potentially inequivalent functions, checkable in the sense of Blum [8, 9, 10]. Up to natural equivalence, only a handful of such functions were previously known; unnatural ones could be obtained by padding and other artificial tricks. Adapting an idea of Beaver and Feigenbaum [6] and Lipton [19] these classes are also shown to have the random self correcting property in ....

....of such functions were previously known; unnatural ones could be obtained by padding and other artificial tricks. Adapting an idea of Beaver and Feigenbaum [6] and Lipton [19] these classes are also shown to have the random self correcting property in the sense of Blum, Luby and Rubinfeld [10]. We also obtain arithmetic straight line program characterizations of PSPACE functions as well as their multilinear extensions. The new technique was motivated by an arithmetization of Boolean formulas obtained by the authors in an attempt to remove permanents from the recent proof by Lund, ....

[Article contains additional citation context not shown here]

M. Blum, M. Luby, and R. Rubinfeld, Self-testing and self-correcting programs, with applications to numerical programs, in Proc. 22nd Ann. ACM Symp. Theory of Computing, 1990, 73-83.

....in nondeterministic exponential time has a two prover interactive proof system in which the provers cannot communicate with one another. Our results also have implications for program checking, verification and self correction in the context of Blum and Kannan [BK] Blum, Luby and Rubinfeld [BLR] and Lipton [L] In fact, the Blum Luby Rubinfeld and Lipton papers inspired our result. Our result does not relativize. Fortnow and Sipser [FS] have created an oracle under which co NP does not have an interactive proof system. To our knowledge this is the first result to go contrary to a ....

....systems. Our theorem also has applications to program checking, verification and self correction. Lipton [L] using ideas of Beaver and Feigenbaum [BeF] showed that the permanent function can be tested. Our protocols extend this idea and show the permanent has a self testing correcting pair [BLR], a pair of functions the first of which verifies that a program computes the permanent correctly on most inputs and the second of which converts a program that passes the first test into one that correctly computes the permanent on all inputs with high probability. Theorem 1 also provides a ....

M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. In Proc. of the 22nd ACM Symp. on the Theory of Computing, 1990.

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M. Blum, M. Luby, and R. Rubinfeld. Self-testing and self-correcting programs, with applications to numerical programs. Journal of Computer and System Sciences, 47:549--595, 1993.

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