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2
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0027206124
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Checking approximate computations over the reals
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Extends checking methodologies to computations on limited-accuracy real numbers. Examples: matrix multiplication, inversion, and determinant; solving systems of linear equations
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S. Ar, M. Blum, B. Codenotti, and P. Gemmell, "Checking approximate computations over the reals," Proc. 25th ACM STOC, pp. 786-795, 1993. Extends checking methodologies to computations on limited-accuracy real numbers. Examples: matrix multiplication, inversion, and determinant; solving systems of linear equations.
-
(1993)
Proc. 25th ACM STOC
, pp. 786-795
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Ar, S.1
Blum, M.2
Codenotti, B.3
Gemmell, P.4
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3
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84968014854
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Probabilistic checking of proofs; a new characterization of NP
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Equates NP languages with those in interactive-proof class PCPlogn, logn
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S. Arora and S. Safra, "Probabilistic checking of proofs; a new characterization of NP," Proc. 33rd IEEE FOCS, pp. 2-13, 1992. Equates NP languages with those in interactive-proof class PCP(logn, logn).
-
(1992)
Proc. 33rd IEEE FOCS
, pp. 2-13
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Arora, S.1
Safra, S.2
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4
-
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0002771903
-
Non-deterministic exponential time has two-prover interactive protocols
-
Proves that NEXP = 2IP, and hence that NEXP-complete problems have complex checkers
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L. Babai, L. Fortnow, and C. Lund, "Non-deterministic exponential time has two-prover interactive protocols," Computational Complexity, Vol. 1, pp. 3-40, 1991. Proves that NEXP = 2IP, and hence that NEXP-complete problems have complex checkers.
-
(1991)
Computational Complexity
, vol.1
, pp. 3-40
-
-
Babai, L.1
Fortnow, L.2
Lund, C.3
-
5
-
-
0002234652
-
Arithmetization: A new method in structural complexity theory
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L. Babai and L. Fortnow, "Arithmetization: a new method in structural complexity theory," Computational Complexity, Vol. 1, pp. 41-46, 1991.
-
(1991)
Computational Complexity
, vol.1
, pp. 41-46
-
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Babai, L.1
Fortnow, L.2
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6
-
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85117105572
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Preliminary version: A characterization of #P by arithmetic straight line programs
-
Further develops a technique from 4 of translating Boolean formulae into multivariate polynomials
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Preliminary version: "A characterization of #P by arithmetic straight line programs," Proc. 31st IEEE FOCS, pp. 26-34, 1990. Further develops a technique from [4] of translating Boolean formulae into multivariate polynomials.
-
(1990)
Proc. 31st IEEE FOCS
, pp. 26-34
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-
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7
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85028539051
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Checking computations in polylogarithmic time
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A variant of 4 with lower time-bounds, this paper introduces an unusual sort of very fast checker for NP computations. Such checkers could be regarded as hardware checkers," in that they ensure that the hardware follows instructions correctly, but don't ensure that the software is correct
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L. Babai, L. Fortnow, L. Levin, and M. Szegedy, "Checking computations in polylogarithmic time," Proc. 23rd ACM STOC, pp. 21-31, 1991. A variant of [4] with lower time-bounds, this paper introduces an unusual sort of very fast checker for NP computations. Such checkers could be regarded as "hardware checkers," in that they ensure that the hardware follows instructions correctly, but don't ensure that the software is correct.
-
(1991)
Proc. 23rd ACM STOC
, pp. 21-31
-
-
Babai, L.1
Fortnow, L.2
Levin, L.3
Szegedy, M.4
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10
-
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0003228498
-
On being incoherent without being very hard
-
Response to questions of 13, 41, including a proof that all NP-complete languages are coherent
-
R. Beigel and J. Feigenbaum, "On being incoherent without being very hard," Computational Complexity, Vol. 2, pp. 1-17, 1992. Response to questions of [13, 41], including a proof that all NP-complete languages are coherent.
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(1992)
Computational Complexity
, vol.2
, pp. 1-17
-
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Beigel, R.1
Feigenbaum, J.2
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12
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85117158556
-
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Avrim Blum, personal communication
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Avrim Blum, personal communication.
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-
-
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13
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5244241001
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Designing programs to check their work
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Introduces result-checking
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M. Blum, "Designing programs to check their work," ICSI Technical Report TR-88-009, 1988. Introduces result-checking.
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(1988)
ICSI Technical Report TR-88-009
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Blum, M.1
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14
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0024867752
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Designing programs that check their work
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M. Blum and S. Kannan, "Designing programs that check their work," Proc. 21st ACM STOC, pp. 86-97, 1989.
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(1989)
Proc. 21st ACM STOC
, pp. 86-97
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Blum, M.1
Kannan, S.2
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15
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0000619172
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Self-testing/correcting with applications to numerical problems
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M. Blum, M. Luby, and R. Rubinfeld, "Self-testing/correcting with applications to numerical problems," Journal of Computer & System Sciences, Vol. 47, pp. 549-95,1993.
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(1993)
Journal of Computer & System Sciences
, vol.47
, pp. 549-595
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-
Blum, M.1
Luby, M.2
Rubinfeld, R.3
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16
-
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23844554379
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Preliminary version
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Introduces self-testers and self-correctors
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Preliminary version: Proc. 22nd ACM STOC, pp. 73-83, 1990. Introduces self-testers and self-correctors.
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(1990)
Proc. 22nd ACM STOC
, pp. 73-83
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-
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17
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0028482823
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Checking the correctness of memories
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Demonstrates that, given a small, secure data base, one may check the correctness of a large, adversarial data base
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M. Blum, W. Evans, P. Gemmell, S. Kannan, and M. Naor, "Checking the correctness of memories," Algorithmica, Vol. 12, pp. 225-244, 1994. Demonstrates that, given a small, secure data base, one may check the correctness of a large, adversarial data base.
-
(1994)
Algorithmica
, vol.12
, pp. 225-244
-
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Blum, M.1
Evans, W.2
Gemmell, P.3
Kannan, S.4
Naor, M.5
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18
-
-
33745992295
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Program result-checking: A theory of testing meets a test of theory
-
Suggests modifications to standard checking definitions for greater utility in real-time, real-number computer systems; in particular, suggests that run-time checks be allowed to repeatedly use stored random bits. With this modification, specifies a simple checker and a fast self-corrector for any linear transformation
-
M. Blum and H. Wasserman, "Program result-checking: a theory of testing meets a test of theory," Proc. 35th IEEE FOCS, 1994. Advocates the use of result-checking as a software-debugging tool. Suggests modifications to standard checking definitions for greater utility in real-time, real-number computer systems; in particular, suggests that run-time checks be allowed to repeatedly use stored random bits. With this modification, specifies a simple checker and a fast self-corrector for any linear transformation.
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Proc. 35th IEEE FOCS, 1994. Advocates the Use of Result-Checking as a Software-Debugging Tool
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Blum, M.1
Wasserman, H.2
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19
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0027306938
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The infeasibility of quantifying the reliability of life-critical real-time software
-
Proves inherent limitations of conventional software testing and of the attempt to assure reliability by running several versions of a program
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R. Butler and G. Finelli, "The infeasibility of quantifying the reliability of life-critical real-time software," IEEE Transactions on Software Engineering, Vol. 19, pp. 3-12, 1993. Proves inherent limitations of conventional software testing and of the attempt to assure reliability by running several versions of a program.
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(1993)
IEEE Transactions on Software Engineering
, vol.19
, pp. 3-12
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Butler, R.1
Finelli, G.2
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20
-
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0342959327
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A note on self-testing/correcting methods for trigonometric functions
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R. Cleve and M. Luby, "A note on self-testing/correcting methods for trigonometric functions," ICSI Technical Report 90-032, 1990.
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(1990)
ICSI Technical Report 90-032
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Cleve, R.1
Luby, M.2
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21
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85117131601
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manuscript, Department of Computer Science, Cornell University, Specifies self-testers for functions including the Fourier Transform
-
Funda Ergün, "Testing multivariate linear functions: overcoming the generator bottleneck," manuscript, Department of Computer Science, Cornell University, 1994. Specifies self-testers for functions including the Fourier Transform.
-
(1994)
Testing Multivariate Linear Functions: Overcoming the Generator Bottleneck
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Ergün, F.1
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22
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0024057387
-
Are there interactive protocols for co-NP languages?
-
Suggests that co-NP may not be contained in IP. 36 later proved the contrary
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L. Fortnow and M. Sipser, "Are there interactive protocols for co-NP languages?" Information Processing Letters, Vol. 28, pp. 249-251, 1988. Suggests that co-NP may not be contained in IP. [36] later proved the contrary.
-
(1988)
Information Processing Letters
, vol.28
, pp. 249-251
-
-
Fortnow, L.1
Sipser, M.2
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24
-
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0001975984
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Self-testing/correcting for polynomials and for approximate functions
-
Commences the extension of traditional checking methodologies to computations on limited-accuracy reals
-
P. Gemmell, R. Lipton, R. Rubinfeld, M. Sudan, and A. Wigderson, "Self-testing/correcting for polynomials and for approximate functions," Proc. 23rd ACM STOC, pp. 32-42, 1991. Commences the extension of traditional checking methodologies to computations on limited-accuracy reals.
-
(1991)
Proc. 23rd ACM STOC
, pp. 32-42
-
-
Gemmell, P.1
Lipton, R.2
Rubinfeld, R.3
Sudan, M.4
Wigderson, A.5
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25
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0000377057
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Highly resilient correctors for polynomials
-
Gives near-optimal self-correctors for programs supposed to compute multivariate polynomials. As long as a program is correct on a 1/2+δfraction of inputs (for δ∈ R+), self-correcting is possible
-
+), self-correcting is possible.
-
(1992)
Information Processing Letters
, vol.43
, pp. 169-174
-
-
Gemmell, P.1
Sudan, M.2
-
26
-
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1542665168
-
-
Ph.D. thesis, Department of Computer Science, University of California, Berkeley, Includes checkers for several hard group-theoretic problems
-
S. Kannan, Program Result-Checking with Applications, Ph.D. thesis, Department of Computer Science, University of California, Berkeley, 1990. Includes checkers for several hard group-theoretic problems.
-
(1990)
Program Result-Checking with Applications
-
-
Kannan, S.1
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28
-
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0003013846
-
New directions in testing, distributed computing and cryptography
-
Proves that #-complete problems have checker/correctors
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R. Lipton, "New directions in testing, distributed computing and cryptography," DIM ACS Series on Discrete Mathematics and Theoretical Computer Science, Vol. 2, pp. 191-202, 1991. Proves that #P-complete problems have checker/correctors.
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(1991)
DIM ACS Series on Discrete Mathematics and Theoretical Computer Science
, vol.2
, pp. 191-202
-
-
Lipton, R.1
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29
-
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0008465874
-
Algebraic methods for interactive proof systems
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C. Lund, L. Fortnow, H. Karloff, and N. Nisan, "Algebraic methods for interactive proof systems," Proc. 31st IEEE FOCS, pp. 2-10, 1990.
-
(1990)
Proc. 31st IEEE FOCS
, pp. 2-10
-
-
Lund, C.1
Fortnow, L.2
Karloff, H.3
Nisan, N.4
-
30
-
-
85117079200
-
Computer science proofs and error-detecting computation
-
MIT Lab for Computer Science Technical Report TM-510, Gives result-checkers for NP-complete problems, subject to the assumptions that we have available a random oracle which can serve as a cryptographically-secure hash-function, and that the program being checked has insufficient time to find collisions in this hash-function
-
S. Micali, "Computer science proofs and error-detecting computation," MIT Lab for Computer Science Technical Report, 1992, and "Computer science proofs," MIT Lab for Computer Science Technical Report TM-510, 1994. Gives result-checkers for NP-complete problems, subject to the assumptions that we have available a random oracle which can serve as a cryptographically-secure hash-function, and that the program being checked has insufficient time to find collisions in this hash-function.
-
(1994)
MIT Lab for Computer Science Technical Report, 1992, and "Computer Science Proofs
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Micali, S.1
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31
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85117076904
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Co-SAT has multi-prover interactive proofs
-
e-mail message, 4
-
N. Nisan, "Co-SAT has multi-prover interactive proofs," e-mail message, 1989. Initiated events leading to [36, 4].
-
(1989)
Initiated Events Leading to
, vol.36
-
-
Nisan, N.1
-
32
-
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0012785603
-
-
Ph.D. thesis, Department of Computer Science, University of California, Berkeley, Incorporates efficient random testing into the run-time checking/correcting process
-
R. Rubinfeld, A Mathematical Theory of Self-Checking, Self-Testing, and Self-Correcting Programs, Ph.D. thesis, Department of Computer Science, University of California, Berkeley, 1990. Incorporates efficient random testing into the run-time checking/correcting process.
-
(1990)
A Mathematical Theory of Self-Checking, Self-Testing, and Self-Correcting Programs
-
-
Rubinfeld, R.1
-
33
-
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0026869838
-
Batch checking with applications to linear functions
-
R. Rubinfeld, "Batch checking with applications to linear functions," Information Processing Letters, Vol. 42, pp. 77-80, 1992.
-
(1992)
Information Processing Letters
, vol.42
, pp. 77-80
-
-
Rubinfeld, R.1
-
34
-
-
85029508009
-
Self-testing polynomial functions efficiently and over rational domains
-
Extends checking methodologies from finite fields to integer and rational domains
-
R. Rubinfeld and M. Sudan, "Self-testing polynomial functions efficiently and over rational domains," Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms, pp. 23-32, 1992. Extends checking methodologies from finite fields to integer and rational domains.
-
(1992)
Proc. 3rd ACM-SIAM Symposium on Discrete Algorithms
, pp. 23-32
-
-
Rubinfeld, R.1
Sudan, M.2
-
35
-
-
33747166413
-
Robust characterizations of polynomials and their applications to program testing
-
R. Rubinfeld and M. Sudan, "Robust characterizations of polynomials and their applications to program testing," IBM Research Report RC19156, 1993, and Cornell Computer Science Technical Report 93-1387, 1993.
-
(1993)
IBM Research Report RC19156, 1993, and Cornell Computer Science Technical Report
, pp. 93-1387
-
-
Rubinfeld, R.1
Sudan, M.2
-
37
-
-
84976779342
-
Fast probabilistic algorithms for verification of polynomial identities
-
A fundamental result: to determine (with high probability) whether two polynomials are identical, it generally suffices to check their equality at a random location. Applications include: testing multiset equality; proving that two straight-line arithmetic programs compute the same function
-
J. Schwartz, "Fast probabilistic algorithms for verification of polynomial identities," Journal of the ACM, Vol. 27, pp. 701-717, 1980. A fundamental result: to determine (with high probability) whether two polynomials are identical, it generally suffices to check their equality at a random location. Applications include: testing multiset equality; proving that two straight-line arithmetic programs compute the same function.
-
(1980)
Journal of the ACM
, vol.27
, pp. 701-717
-
-
Schwartz, J.1
-
38
-
-
0002750721
-
IP = pspace
-
It follows from this result that all PSPACE-complete problems have complex checkers
-
A. Shamir, "IP = PSPACE," Proc. 31st IEEE FOCS, pp. 11-15, 1990. It follows from this result that all PSPACE-complete problems have complex checkers.
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(1990)
Proc. 31st IEEE FOCS
, pp. 11-15
-
-
Shamir, A.1
-
39
-
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84922420885
-
Error detection and correction in numerical computations by algebraic methods
-
Springer- Verlag Lecture Notes in Computer Science #539
-
F. Vainstein, "Error detection and correction in numerical computations by algebraic methods," Proc. 9th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Detecting Codes, 1991. Springer- Verlag Lecture Notes in Computer Science #539, pp. 456-464, 1991.
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(1991)
Proc. 9th International Symposium on Applied Algebra, Algebraic Algorithms and Error-Detecting Codes, 1991
, pp. 456-464
-
-
Vainstein, F.1
-
40
-
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0008962903
-
-
Ph.D. thesis, EECS Department, Boston University, Uses the theory of algebraic and transcendental fields to design partial complex checkers for rational functions constructed from x, ex, sin(ax + b), and cos(ax + 6) using operators + x/and fractional exponentiation
-
x, sin(ax + b), and cos(ax + 6) using operators + - x/and fractional exponentiation.
-
(1993)
Algebraic Methods in Hardware/Software Testing
-
-
Vainstein, F.1
-
41
-
-
49249151236
-
The complexity of computing the permanent
-
Defines #-completeness and proves that computing the permanent of a matrix is #-complete. Also 26
-
L. Valiant, "The complexity of computing the permanent," Theoretical Computer Science, Vol. 8, pp. 189-201, 1979. Defines #P-completeness and proves that computing the permanent of a matrix is #P-complete. Also see [26].
-
(1979)
Theoretical Computer Science
, vol.8
, pp. 189-201
-
-
Valiant, L.1
-
42
-
-
0019572642
-
New hash functions and their use in authentication and set equality
-
Includes an idea for a simple check of multiset equality completed in 12
-
M. Wegman and J. Carter, "New hash functions and their use in authentication and set equality," Journal of Computer & System Sciences, Vol. 22, pp. 265-279, 1981. Includes an idea for a simple check of multiset equality (completed in [12]).
-
(1981)
Journal of Computer & System Sciences
, vol.22
, pp. 265-279
-
-
Wegman, M.1
Carter, J.2
-
43
-
-
0024984430
-
Coherent functions and program checkers
-
Function f is coherent iff on input (x, y) one can determine whether or not f(x) = y via a BPP; algorithm which is not allowed to query f at x. Author proves the existence of incoherent (and thus uncheckable) functions in EXP. also 9
-
; algorithm which is not allowed to query f at x. Author proves the existence of incoherent (and thus uncheckable) functions in EXP. See also [9].
-
(1990)
Proc. 22nd ACM STOC
, pp. 84-94
-
-
Yao, A.1
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