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Volumn 16, Issue 2, 2007, Pages 115-138

Polynomial identity testing for depth 3 circuits

Author keywords

Chinese remaindering; Depth of circuits; Identity testing; Rings

Indexed keywords


EID: 34249038395     PISSN: 10163328     EISSN: 14208954     Source Type: Journal    
DOI: 10.1007/s00037-007-0226-9     Document Type: Conference Paper
Times cited : (77)

References (20)
  • 1
    • 15944413051 scopus 로고    scopus 로고
    • Primality and identity testing via Chinese remaindering
    • M. AGRAWAL & S. BISWAS (2003). Primality and identity testing via Chinese remaindering. Journal of the ACM 50(4), 429-443.
    • (2003) Journal of the ACM , vol.50 , Issue.4 , pp. 429-443
    • AGRAWAL, M.1    BISWAS, S.2
  • 3
    • 0033701650 scopus 로고    scopus 로고
    • Reducing Randomness via Irrational Numbers
    • Z. CHEN & M. KAO (2000). Reducing Randomness via Irrational Numbers. SIAM Journal of Computing 29(4), 1247-1256.
    • (2000) SIAM Journal of Computing , vol.29 , Issue.4 , pp. 1247-1256
    • CHEN, Z.1    KAO, M.2
  • 6
    • 0033699197 scopus 로고    scopus 로고
    • Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields
    • D. GRIGORIEV & A. A. RAZBOROV (2000). Exponential Lower Bounds for Depth 3 Arithmetic Circuits in Algebras of Functions over Finite Fields. Appl. Algebra Eng. Commun. Comput. 10(6), 465-487.
    • (2000) Appl. Algebra Eng. Commun. Comput , vol.10 , Issue.6 , pp. 465-487
    • GRIGORIEV, D.1    RAZBOROV, A.A.2
  • 7
    • 15244352005 scopus 로고    scopus 로고
    • Derandomizing polynomial identity tests means proving circuit lower bounds
    • R. IMPAGLIAZZO & V. KABANETS (2004). Derandomizing polynomial identity tests means proving circuit lower bounds. Computational Complexity 13(1/2), 1-46.
    • (2004) Computational Complexity , vol.13 , Issue.1-2 , pp. 1-46
    • IMPAGLIAZZO, R.1    KABANETS, V.2
  • 8
    • 0020160366 scopus 로고
    • Some Exact Complexity Results for Straight-Line Computations over Semirings
    • M. JERRUM & M. SNIR (1982). Some Exact Complexity Results for Straight-Line Computations over Semirings. Journal of the ACM 29(3), 874-897.
    • (1982) Journal of the ACM , vol.29 , Issue.3 , pp. 874-897
    • JERRUM, M.1    SNIR, M.2
  • 12
    • 0001013907 scopus 로고
    • Communication in Bounded Depth Circuits
    • P. PUDLÁK (1994). Communication in Bounded Depth Circuits. Combinatorica 14(2), 203-216.
    • (1994) Combinatorica , vol.14 , Issue.2 , pp. 203-216
    • PUDLÁK, P.1
  • 14
    • 18244365341 scopus 로고    scopus 로고
    • Deterministic polynomial identity testing in non-commutative models
    • R. RAZ & A. SHPILKA (2005). Deterministic polynomial identity testing in non-commutative models. Computational Complexity 14(1), 1-19.
    • (2005) Computational Complexity , vol.14 , Issue.1 , pp. 1-19
    • RAZ, R.1    SHPILKA, A.2
  • 15
    • 84976779342 scopus 로고
    • Fast Probabilistic Algorithms for Verification of Polynomial Identities
    • J. T. SCHWARTZ (1980). Fast Probabilistic Algorithms for Verification of Polynomial Identities. Journal of the ACM 27(4), 701-717.
    • (1980) Journal of the ACM , vol.27 , Issue.4 , pp. 701-717
    • SCHWARTZ, J.T.1
  • 16
    • 33645254013 scopus 로고
    • Lower bounds on the number of multiplications and the number of additions in monotone computations
    • RC6757
    • E. SHAMIR & M. SNIR (1977). Lower bounds on the number of multiplications and the number of additions in monotone computations. Research Report RC6757.
    • (1977) Research Report
    • SHAMIR, E.1    SNIR, M.2
  • 17
  • 18
    • 0035729224 scopus 로고    scopus 로고
    • Depth-3 arithmetic circuits over fields of characteristic zero
    • A. SHPILKA & A. WIGDERSON (2001). Depth-3 arithmetic circuits over fields of characteristic zero. Computational Complexity 10(1), 1-27.
    • (2001) Computational Complexity , vol.10 , Issue.1 , pp. 1-27
    • SHPILKA, A.1    WIGDERSON, A.2
  • 19
    • 0028392060 scopus 로고
    • A Direct Version of Shamir and Snir's Lower Bounds on Monotone Circuit Depth
    • P. TIWARI & M. TOMPA (1994). A Direct Version of Shamir and Snir's Lower Bounds on Monotone Circuit Depth. Information Processing Letters 49(5), 243-248.
    • (1994) Information Processing Letters , vol.49 , Issue.5 , pp. 243-248
    • TIWARI, P.1    TOMPA, M.2
  • 20
    • 84925463455 scopus 로고
    • Probabilistic Algorithms for Sparse Polynomials
    • International Symposium on Symbolic and Algebraic Computation, of, Springer-Verlag
    • R. ZIPPEL (1979). Probabilistic Algorithms for Sparse Polynomials. In International Symposium on Symbolic and Algebraic Computation, volume 72 of Lecture Notes in Computer Science, 216-226. Springer-Verlag.
    • (1979) Lecture Notes in Computer Science , vol.72 , pp. 216-226
    • ZIPPEL, R.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.