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Volumn , Issue , 2005, Pages 592-601

Locally decodable codes with 2 queries and polynomial identity testing for depth 3 circuits

Author keywords

Depth 3 circuits; Locally decodable codes; Polynomial identity testing

Indexed keywords

ALGORITHMS; DECODING; POLYNOMIALS; QUERY LANGUAGES; SET THEORY;

EID: 33751057316     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1060590.1060678     Document Type: Conference Paper
Times cited : (25)

References (49)
  • 1
    • 15944413051 scopus 로고    scopus 로고
    • Primality and identity testing via Chinese remaindering
    • Manindra Agrawal and Somenath Biswas. Primality and identity testing via Chinese remaindering. J. ACM, 50(4):429-443, 2003.
    • (2003) J. ACM , vol.50 , Issue.4 , pp. 429-443
    • Agrawal, M.1    Biswas, S.2
  • 3
    • 30744469433 scopus 로고    scopus 로고
    • A unifying approach for proving hardcore predicates using list decoding
    • Cambridge, MA, USA
    • Adi Akavia, Shafi Goldwasser, and Muli Safra. A unifying approach for proving hardcore predicates using list decoding. In 44th FOCS, pages 146-155, Cambridge, MA, USA, 2003.
    • (2003) 44th FOCS , pp. 146-155
    • Akavia, A.1    Goldwasser, S.2    Safra, M.3
  • 4
    • 85028539051 scopus 로고
    • Checking computations in polylogarithmic time
    • ACM Press
    • László Babai. Lance Fortnow, Leonid A. Levin, and Mario Szegedy. Checking computations in polylogarithmic time. In 23rd STOC, pages 21-32. ACM Press, 1991.
    • (1991) 23rd STOC , pp. 21-32
    • Babai, L.1    Fortnow, L.2    Levin, L.A.3    Szegedy, M.4
  • 5
    • 0005478995 scopus 로고
    • The complexity of partial derivatives
    • Walter Baur and Volker Strassen. The complexity of partial derivatives. Theoretical Computer Science, 22:317 - 330, 1983.
    • (1983) Theoretical Computer Science , vol.22 , pp. 317-330
    • Baur, W.1    Strassen, V.2
  • 6
    • 33745511846 scopus 로고
    • Hiding instances in multioracle queries
    • Springer-Verlag New York, Inc.
    • Donald Beaver and J. Feigenbaum. Hiding instances in multioracle queries. In STACS '90, pages 37-48. Springer-Verlag New York, Inc., 1990.
    • (1990) STACS '90 , pp. 37-48
    • Beaver, D.1    Feigenbaum, J.2
  • 7
    • 84879524288 scopus 로고    scopus 로고
    • Information-theoretic private information retrieval: A unified construction
    • Amos Beimel and Yuval Ishai. Information-theoretic private information retrieval: A unified construction. Lecture Notes in Computer Science, 2076:912-926, 2001.
    • (2001) Lecture Notes in Computer Science , vol.2076 , pp. 912-926
    • Beimel, A.1    Ishai, Y.2
  • 9
    • 84898974734 scopus 로고
    • A deterministic algorithm for sparse multivariate polynomial interpolation
    • ACM Press
    • Michael Ben-Or and Prasoon Tiwari. A deterministic algorithm for sparse multivariate polynomial interpolation. In 20th STOC, pages 301-309. ACM Press, 1988.
    • (1988) 20th STOC , pp. 301-309
    • Ben-Or, M.1    Tiwari, P.2
  • 10
    • 0024715662 scopus 로고
    • A lower bound for matrix multiplication
    • Nader H. Bshouty. A lower bound for matrix multiplication. SIAM J. Comput., 18(4):759-765, 1989.
    • (1989) SIAM J. Comput. , vol.18 , Issue.4 , pp. 759-765
    • Bshouty, N.H.1
  • 11
    • 0029499709 scopus 로고
    • Randomness-optimal unique element isolation withapplications to perfect matching and related problems
    • Suresh Chari, Pankaj Rohatgi, and Aravind Srinivasan. Randomness-optimal unique element isolation withapplications to perfect matching and related problems. SIAM J. Comput., 24(5):1036-1050. 1995.
    • (1995) SIAM J. Comput. , vol.24 , Issue.5 , pp. 1036-1050
    • Chari, S.1    Rohatgi, P.2    Srinivasan, A.3
  • 12
    • 0030645679 scopus 로고    scopus 로고
    • Reducing randomness via irrational numbers
    • ACM Press
    • Zhi-Zhong Chen and Ming-Yang Kao. Reducing randomness via irrational numbers. In 29th STOC, pages 200-209. ACM Press, 1997.
    • (1997) 29th STOC , pp. 200-209
    • Chen, Z.-Z.1    Kao, M.-Y.2
  • 14
    • 0036287481 scopus 로고    scopus 로고
    • Better lower bounds for locally decodable codes
    • IEEE Computer Society
    • Amit Deshpande, Rahul Jain, T Kavitha, Jaikumar Radhakrishnan, and Satyanarayana V. Lokam. Better lower bounds for locally decodable codes. In CCC '02, page 184. IEEE Computer Society, 2002.
    • (2002) CCC '02 , pp. 184
    • Deshpande, A.1    Jain, R.2    Kavitha, T.3    Radhakrishnan, J.4    Lokam, S.V.5
  • 15
    • 0027684980 scopus 로고
    • Random-self-reducibility of complete sets
    • Joan Feigenbaum and Lance Fortnow. Random-self-reducibility of complete sets. SIAM J. Comput., 22(5):994-1005, 1993.
    • (1993) SIAM J. Comput. , vol.22 , Issue.5 , pp. 994-1005
    • Feigenbaum, J.1    Fortnow, L.2
  • 16
    • 0001975984 scopus 로고
    • Self-testing/correcting for polynomials and for approximate functions
    • ACM Press
    • Peter Gemmell, Richard J. Lipton, Ronitt Rubinfeld, Madhu Sudan, and Avi Wigderson. Self-testing/correcting for polynomials and for approximate functions. In 23rd STOC, pages 33-42. ACM Press, 1991.
    • (1991) 23rd STOC , pp. 33-42
    • Gemmell, P.1    Lipton, R.J.2    Rubinfeld, R.3    Sudan, M.4    Wigderson, A.5
  • 17
    • 0000377057 scopus 로고
    • Highly resilient correctors for polynomials
    • Peter Gemmell and Madhu Sudan. Highly resilient correctors for polynomials. Information Processing Letters, 43(4):169-174, 1992.
    • (1992) Information Processing Letters , vol.43 , Issue.4 , pp. 169-174
    • Gemmell, P.1    Sudan, M.2
  • 18
    • 0036287480 scopus 로고    scopus 로고
    • Lower bounds for linear locally decodable codes and private information retrieval
    • IEEE Computer Society
    • Oded Goldreich, Howard Karloff, Leonard J. Schulman, and Luca Trevisan. Lower bounds for linear locally decodable codes and private information retrieval. In CCC '02, page 175. IEEE Computer Society, 2002.
    • (2002) CCC '02 , pp. 175
    • Goldreich, O.1    Karloff, H.2    Schulman, L.J.3    Trevisan, L.4
  • 19
    • 0024868772 scopus 로고
    • A hardcore predicate for all oneway functions
    • Seattle. Washington, USA
    • Oded Goldreich and Leonid A. Levin. A hardcore predicate for all oneway functions. In 21st STOC, pages 25-32, Seattle. Washington, USA, 1989.
    • (1989) 21st STOC , pp. 25-32
    • Goldreich, O.1    Levin, L.A.2
  • 21
    • 0031639854 scopus 로고    scopus 로고
    • An exponential lower bound for depth 3 arithmetic circuits
    • ACM Press
    • Dima Grigoriev and Marek Karpinski. An exponential lower bound for depth 3 arithmetic circuits. In 30th STOC, pages 577-582. ACM Press, 1998.
    • (1998) 30th STOC , pp. 577-582
    • Grigoriev, D.1    Karpinski, M.2
  • 22
    • 0025694134 scopus 로고
    • Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
    • Dima Grigoriev. Marek Karpinski, and Michael F. Singer. Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. SIAM J. Comput., 19(6):1059-1063, 1990.
    • (1990) SIAM J. Comput. , vol.19 , Issue.6 , pp. 1059-1063
    • Karpinski, D.G.M.1    Singer, M.F.2
  • 23
    • 0032314452 scopus 로고    scopus 로고
    • Exponential complexity lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields
    • Dima Grigoriev and Alexander A. Razborov. Exponential complexity lower bounds for depth 3 arithmetic circuits in algebras of functions over finite fields. In 39th FOCS, pages 269-278, 1998.
    • (1998) 39th FOCS , pp. 269-278
    • Grigoriev, D.1    Razborov, A.A.2
  • 24
    • 30744448725 scopus 로고
    • Some exact complexity results for straight-line computations over semi-rings
    • Univ. of Edinburgh
    • Mark Jerrum and Marc Snir. Some exact complexity results for straight-line computations over semi-rings. Technical Report CRS-58-80, Univ. of Edinburgh, 1980.
    • (1980) Technical Report , vol.CRS-58-80
    • Jerrum, M.1    Snir, M.2
  • 25
    • 0038107689 scopus 로고    scopus 로고
    • Derandomizing polynomial identity tests means proving circuit lower bounds
    • ACM Press
    • Valentine Kabanets and Russell Impagliazzo. Derandomizing polynomial identity tests means proving circuit lower bounds. In 35th STOC, pages 355-364. ACM Press, 2003.
    • (2003) 35th STOC , pp. 355-364
    • Kabanets, V.1    Impagliazzo, R.2
  • 26
    • 0033720713 scopus 로고    scopus 로고
    • On the efficiency of local decoding procedures for error-correcting codes
    • ACM Press
    • Jonathan Katz and Luca Trevisan. On the efficiency of local decoding procedures for error-correcting codes. In 32nd STOC, pages 80-86. ACM Press, 2000.
    • (2000) 32nd STOC , pp. 80-86
    • Katz, J.1    Trevisan, L.2
  • 27
    • 0038107747 scopus 로고    scopus 로고
    • Exponential lower bound for 2-query locally decodable codes via a quantum argument
    • ACM Press
    • Iordanis Kerenidis and Ronald de Wolf. Exponential lower bound for 2-query locally decodable codes via a quantum argument. In 35th STOC, pages 106-115. ACM Press, 2003.
    • (2003) 35th STOC , pp. 106-115
    • Kerenidis, I.1    De Wolf, R.2
  • 28
    • 0034825851 scopus 로고    scopus 로고
    • Randomness efficient identity testing of multivariate polynomials
    • ACM Press
    • Adam R. Klivans and Daniel Spielman. Randomness efficient identity testing of multivariate polynomials. In 33rd STOC, pages 216-223. ACM Press, 2001.
    • (2001) 33rd STOC , pp. 216-223
    • Klivans, A.R.1    Spielman, D.2
  • 29
    • 51249173191 scopus 로고
    • One-way functions and pseudorandom generators
    • Leonid A. Levin. One-way functions and pseudorandom generators. Combinatorica, 7(4):357-363, 1987.
    • (1987) Combinatorica , vol.7 , Issue.4 , pp. 357-363
    • Levin, L.A.1
  • 30
    • 0031625441 scopus 로고    scopus 로고
    • Checking polynomial identities over any field: Towards a derandomization?
    • ACM Press
    • Daniel Lewin and Salil Vadhan. Checking polynomial identities over any field: towards a derandomization? In 30th STOC, pages 438-447. ACM Press, 1998.
    • (1998) 30th STOC , pp. 438-447
    • Lewin, D.1    Vadhan, S.2
  • 31
    • 85032506453 scopus 로고
    • Efficient checking of computations
    • C. Choffrut and T. Lengauer, editors. Springer. Berlin, Heidelberg
    • Richard J. Lipton. Efficient checking of computations. In C. Choffrut and T. Lengauer, editors, STAGS 90, pages 207-215. Springer. Berlin, Heidelberg, 1990.
    • (1990) STAGS 90 , pp. 207-215
    • Lipton, R.J.1
  • 33
    • 0023569163 scopus 로고
    • Matching is as easy as matrix inversion
    • ACM Press
    • Ketan Mulmuley, Umesh V. Vazirani, and Vijay V. Vazirani. Matching is as easy as matrix inversion. In 19th STOC, pages 345-354. ACM Press, 1987.
    • (1987) 19th STOC , pp. 345-354
    • Mulmuley, K.1    Vazirani, U.V.2    Vazirani, V.V.3
  • 34
    • 85000547940 scopus 로고
    • Lower bounds for non-commutative computation
    • ACM Press
    • Noam Nisan. Lower bounds for non-commutative computation. In 23rd STOC, pages 410-418. ACM Press, 1991.
    • (1991) 23rd STOC , pp. 410-418
    • Nisan, N.1
  • 35
    • 0029519805 scopus 로고
    • Lower bounds for arithmetic circuits via partial serivatives (preliminary version)
    • Noam Nisan and Avi Wigderson. Lower bounds for arithmetic circuits via partial serivatives (preliminary version). In 36th FOCS, pages 16-25, 1995.
    • (1995) 36th FOCS , pp. 16-25
    • Nisan, N.1    Wigderson, A.2
  • 37
    • 0001013907 scopus 로고
    • Communication in bounded depth circuits
    • Pavel Pudlak. Communication in bounded depth circuits. Combinatorica, 14(2):203-216, 1994.
    • (1994) Combinatorica , vol.14 , Issue.2 , pp. 203-216
    • Pudlak, P.1
  • 38
    • 4544258177 scopus 로고    scopus 로고
    • Multi-linear formulas for permanent and determinant are of super-polynomial size
    • ACM Press
    • Ran Raz. Multi-linear formulas for permanent and determinant are of super-polynomial size. In 36th STOC, pages 633-641. ACM Press, 2004.
    • (2004) 36th STOC , pp. 633-641
    • Raz, R.1
  • 39
    • 4944248533 scopus 로고    scopus 로고
    • Deterministic polynomial identity testing in non commutative models
    • Ran Raz and Aamir Shpilka. Deterministic polynomial identity testing in non commutative models. CCC '04, 2004.
    • (2004) CCC '04
    • Raz, R.1    Shpilka, A.2
  • 40
    • 0034834489 scopus 로고    scopus 로고
    • Lower bounds for matrix product, in bounded depth circuits with arbitrary gates
    • ACM Press
    • Ran Raz and Amir Shpilka. Lower bounds for matrix product, in bounded depth circuits with arbitrary gates. In 33rd STOC, pages 409-418. ACM Press, 2001.
    • (2001) 33rd STOC , pp. 409-418
    • Raz, R.1    Shpilka, A.2
  • 41
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • Jacob T. Schwartz. Fast probabilistic algorithms for verification of polynomial identities. J. ACM, 27(4):701-717, 1980.
    • (1980) J. ACM , vol.27 , Issue.4 , pp. 701-717
    • Schwartz, J.T.1
  • 42
    • 33645254013 scopus 로고
    • Lower bounds on the number of multiplications and the number of additions in monotone computations
    • IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., sep
    • Eli Shamir and Marc Snir. Lower bounds on the number of multiplications and the number of additions in monotone computations. Research Report RC6757, IBM Thomas J. Watson Research Center, Yorktown Heights, N.Y., sep 1977.
    • (1977) Research Report , vol.RC6757
    • Shamir, E.1    Snir, M.2
  • 43
    • 0039045277 scopus 로고
    • On the depth complexity of formulas
    • Eli Shamir and Marc Snir. On the depth complexity of formulas. Mathematical Systems Theory, 13:301-322, 1980.
    • (1980) Mathematical Systems Theory , vol.13 , pp. 301-322
    • Shamir, E.1    Snir, M.2
  • 44
    • 0345015878 scopus 로고    scopus 로고
    • Lower bounds for matrix product
    • Amir Shpilka. Lower bounds for matrix product. SIAM J. Comput., 32(5):1185-1200, 2003.
    • (2003) SIAM J. Comput. , vol.32 , Issue.5 , pp. 1185-1200
    • Shpilka, A.1
  • 45
    • 0032644925 scopus 로고    scopus 로고
    • Depth-3 arithmetic formulae over fields of characteristic zero
    • IEEE Computer Society
    • Amir Shpilka and Avi Wigderson. Depth-3 arithmetic formulae over fields of characteristic zero. In CCC '99, page 87. IEEE Computer Society, 1999.
    • (1999) CCC '99 , pp. 87
    • Shpilka, A.1    Wigderson, A.2
  • 46
    • 0001063303 scopus 로고
    • Die berechnungskomplexitat vo elementarsymmetrischen funktionen und von interpolationskoefizienten
    • Volker Strassen. Die berechnungskomplexitat vo elementarsymmetrischen funktionen und von interpolationskoefizienten. Numer. Math, 20:238-251, 1973.
    • (1973) Numer. Math , vol.20 , pp. 238-251
    • Strassen, V.1
  • 47
    • 0028392060 scopus 로고
    • A direct version of shamir and snir's lower bounds on monotone circuit depth
    • Prasoon Tiwari and Martin Tompa. A direct version of shamir and snir's lower bounds on monotone circuit depth. Inf. Process. Lett., 49(5):243-248, 1994.
    • (1994) Inf. Process. Lett. , vol.49 , Issue.5 , pp. 243-248
    • Tiwari, P.1    Tompa, M.2
  • 49
    • 84925463455 scopus 로고
    • Probabilistic algorithms for sparse polynomials
    • Springer-Verlag
    • Richard Zippel. Probabilistic algorithms for sparse polynomials. In ISSAC '79, pages 216-226. Springer-Verlag, 1979.
    • (1979) ISSAC '79 , pp. 216-226
    • Zippel, R.1


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