메뉴 건너뛰기




Volumn 57, Issue 4, 2010, Pages

Simulating independence: New constructions of condensers, ramsey graphs, dispersers, and extractors

Author keywords

Condensers; Dispersers; Explicit constructions; Extractors; Ramsey graphs

Indexed keywords

BINARY STRING; BUILDING BLOCKES; CHALLENGE RESPONSE; COMPLETE BIPARTITE GRAPHS; COMPUTABLE FUNCTIONS; EXPLICIT CONSTRUCTIONS; INDUCED SUBGRAPHS; NEW CONSTRUCTION; OPEN PROBLEMS; RANDOMNESS EXTRACTORS; SOURCE EXTRACTOR; TWO SOURCES;

EID: 77952022169     PISSN: 00045411     EISSN: 1557735X     Source Type: Journal    
DOI: 10.1145/1734213.1734214     Document Type: Article
Times cited : (49)

References (40)
  • 1
    • 34247566037 scopus 로고    scopus 로고
    • Extracting randomness using few independent sources
    • Preliminary version in FOCS '04
    • BARAK, B., IMPAGLIAZZO, R., AND WIGDERSON, A. 2006a. Extracting randomness using few independent sources. SIAM J. Comput 36, 4, 1095-1118. (Preliminary version in FOCS '04).
    • (2006) SIAM J. Comput , vol.36 , Issue.4 , pp. 1095-1118
    • Barak, B.1    Impagliazzo, R.2    Wigderson, A.3
  • 3
    • 33745861377 scopus 로고    scopus 로고
    • True random number generators secure in a changing environment
    • Lecture Notes in Computer Science Springer-Verlag, Berlin, Germany
    • BARAK, B., SHALTIEL, R., AND TROMER, E. 2003. True random number generators secure in a changing environment. In Proceedings of the Workshop on Cryptographic Hardware and Embedded Systems (CHES). Lecture Notes in Computer Science, vol. 2779. Springer-Verlag, Berlin, Germany. 166-180.
    • (2003) Proceedings of the Workshop on Cryptographic Hardware and Embedded Systems (CHES) , vol.2779 , pp. 166-180
    • Barak, B.1    Shaltiel, R.2    Tromer, E.3
  • 5
    • 51249178917 scopus 로고
    • Independent unbiased coin flips from a correlated biased source-A finite state markov chain
    • BLUM,M. 1986. Independent unbiased coin flips from a correlated biased source-A finite state markov chain. Combinatorica 6, 2, 97-108.
    • (1986) Combinatorica , vol.6 , Issue.2 , pp. 97-108
    • Blum, M.1
  • 6
    • 33746365070 scopus 로고    scopus 로고
    • More on the sum-product phenomenon in prime fields and its applications
    • BOURGAIN, J. 2005. More on the sum-product phenomenon in prime fields and its applications. Int. J. Numb. Theory 1, 1-32.
    • (2005) Int. J. Numb. Theory , vol.1 , pp. 1-32
    • Bourgain, J.1
  • 7
    • 2442427378 scopus 로고    scopus 로고
    • A sum-product estimate in finite fields, and applications
    • BOURGAIN, J., KATZ, N., AND TAO, T. 2004. A sum-product estimate in finite fields, and applications. Geom. Funct. Anal. 14, 1, 27-57.
    • (2004) Geom. Funct. Anal. , vol.14 , Issue.1 , pp. 27-57
    • Bourgain, J.1    Katz, N.2    Tao, T.3
  • 9
    • 0023985259 scopus 로고
    • Unbiased bits from sources of weak randomness and probabilistic communication complexity
    • CHOR, B., AND GOLDREICH, O. 1988. Unbiased bits from sources of weak randomness and probabilistic communication complexity. SIAM J. Comput. 17, 2, 230-261.
    • (1988) SIAM J. Comput. , vol.17 , Issue.2 , pp. 230-261
    • Chor, B.1    Goldreich, O.2
  • 14
    • 51249185135 scopus 로고
    • Intersection theorems with geometric consequences
    • FRANKL, P., AND WILSON, R. M. 1981. Intersection theorems with geometric consequences. Combinatorica 1, 4, 357-368.
    • (1981) Combinatorica , vol.1 , Issue.4 , pp. 357-368
    • Frankl, P.1    Wilson, R.M.2
  • 15
    • 34547843024 scopus 로고    scopus 로고
    • Deterministic extractors for bit-fixing sources by obtaining an independent seed
    • Preliminary version in FOCS '04
    • GABIZON, A., RAZ, R., AND SHALTIEL, R. 2006. Deterministic extractors for bit-fixing sources by obtaining an independent seed. SIAM J. Comput. 36, 4, 1072-1094. (Preliminary version in FOCS '04).
    • (2006) SIAM J. Comput. , vol.36 , Issue.4 , pp. 1072-1094
    • Gabizon, A.1    Raz, R.2    Shaltiel, R.3
  • 18
    • 68549120859 scopus 로고    scopus 로고
    • Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes
    • Preliminary version in CCC '07
    • GURUSWAMI, V.,UMANS, C., AND VADHAN, S. 2009. Unbalanced expanders and randomness extractors from Parvaresh-Vardy codes. J. ACM 56, 4, 20. (Preliminary version in CCC '07).
    • (2009) J. ACM , vol.56 , Issue.4 , pp. 20
    • Guruswami, V.1    Umans, C.2    Vadhan, S.3
  • 19
    • 35448977790 scopus 로고    scopus 로고
    • Deterministic extractors for bit-fixing sources and exposureresilient cryptography
    • Preliminary version in STOC '06
    • KAMP, J., AND ZUCKERMAN, D. 2007. Deterministic extractors for bit-fixing sources and exposureresilient cryptography. SIAM J. Comput. 36, 5, 1231-1247. (Preliminary version in STOC '06).
    • (2007) SIAM J. Comput. , vol.36 , Issue.5 , pp. 1231-1247
    • Kamp, J.1    Zuckerman, D.2
  • 22
    • 84977114496 scopus 로고
    • On the impossibility of private key cryptography with weakly random keys
    • Lecture Notes in Computer Science Springer- Verlag, Berlin, Germany
    • MCINNES, J. L., AND PINKAS, B. 1990. On the impossibility of private key cryptography with weakly random keys. In Proceedings of Crypto '90. Lecture Notes in Computer Science, vol. 537. Springer- Verlag, Berlin, Germany, 421-436.
    • (1990) Proceedings of Crypto '90 , vol.537 , pp. 421-436
    • McInnes, J.L.1    Pinkas, B.2
  • 23
    • 23844490169 scopus 로고    scopus 로고
    • On the complexity of approximating the VC dimension
    • DOI 10.1016/S0022-0000(02)00022-3, PII S0022000002000223
    • MOSSEL, E., AND UMANS, C. 2002. On the complexity of approximating the VC dimension. J. Comput. Syst. Sci. 65, 4, 660-671. (Preliminary version in CCC '01). (Pubitemid 41161944)
    • (2003) Journal of Computer and System Sciences , vol.65 , Issue.4 , pp. 660-671
    • Mossel, E.1    Umans, C.2
  • 24
    • 77952052663 scopus 로고    scopus 로고
    • On explicit ramsey graphs and estimates on the numbers of sums and products
    • Springer-Verlag, Berlin, Germany
    • PUDLAK, P. 2006. On explicit ramsey graphs and estimates on the numbers of sums and products. In Topics in Discrete Mathematics, Algorithms Combin. Vol. 26. Springer-Verlag, Berlin, Germany, 169-175.
    • (2006) Topics in Discrete Mathematics, Algorithms Combin. , vol.26 , pp. 169-175
    • Pudlak, P.1
  • 25
    • 33750330247 scopus 로고    scopus 로고
    • Pseudorandom sets and explicit constructions of ramsey graphs
    • Quad. Mat. Dept. Math., Seconda Univ. Napoli, Caserta
    • PUDĹAK, P., AND RÖDL, V. 2004. Pseudorandom sets and explicit constructions of ramsey graphs. In Complexity of Computations and Proofs. Quad. Mat., 13, Dept. Math., Seconda Univ. Napoli, Caserta, 327-346.
    • (2004) Complexity of Computations and Proofs , vol.13 , pp. 327-346
    • Pudĺak, P.1    Rödl, V.2
  • 26
    • 33748105465 scopus 로고    scopus 로고
    • Extractors for a constant number of polynomially small min-entropy independent sources
    • ACM,NewYork
    • RAO,A. 2006. Extractors for a constant number of polynomially small min-entropy independent sources. In Proceedings of the 38th Annual ACMSymposium on Theory of Computing.ACM,NewYork, 497-506.
    • (2006) Proceedings of the 38th Annual ACMSymposium on Theory of Computing , pp. 497-506
    • Rao, A.1
  • 29
    • 33750154710 scopus 로고    scopus 로고
    • Extracting randomness via repeated condensing
    • Preliminary version in FOCS '00
    • REINGOLD, O., SHALTIEL, R., ANDWIGDERSON, A. 2006. Extracting randomness via repeated condensing. SIAM J. Comput. 35, 5, 1185-1209. (Preliminary version in FOCS '00).
    • (2006) SIAM J. Comput. , vol.35 , Issue.5 , pp. 1185-1209
    • Reingold, O.1    Shaltiel, R.2    Wigderson, A.3
  • 30
    • 0036000527 scopus 로고    scopus 로고
    • Entropy waves, the zig-zag graph product, and new constant-degree expanders
    • Preliminary vesion in FOCS 00
    • REINGOLD, O., VADHAN, S. P., AND WIGDERSON, A. 2002. Entropy waves, the zig-zag graph product, and new constant-degree expanders. Ann. Math. 155, 1, 157-187. (Preliminary vesion in FOCS '00).
    • (2002) Ann. Math. , vol.155 , Issue.1 , pp. 157-187
    • Reingold, O.1    Vadhan, S.P.2    Wigderson, A.3
  • 34
    • 34248175874 scopus 로고    scopus 로고
    • Lossless condensers, unbalanced expanders, and extractors
    • TA-SHMA, A.,UMANS, C., AND ZUCKERMAN, D. 2007. Lossless condensers, unbalanced expanders, and extractors. Combinatorica 27, 2, 213-240.
    • (2007) Combinatorica , vol.27 , Issue.2 , pp. 213-240
    • Ta-Shma, A.1    Umans, C.2    Zuckerman, D.3
  • 35
    • 33845302486 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge, MA
    • TAO, T. AND VU, V. 2006. Additive combinatorics. Cambridge University Press, Cambridge, MA.
    • (2006) Additive Combinatorics
    • Tao, T.1    Vu, V.2
  • 37
    • 51249175241 scopus 로고
    • Strong communication complexity or generating quasi-random sequences from two communicating semi-random sources
    • VAZIRANI, U. 1987. Strong communication complexity or generating quasi-random sequences from two communicating semi-random sources. Combinatorica 7, 4.
    • (1987) Combinatorica , vol.7 , pp. 4
    • Vazirani, U.1
  • 38
    • 0003087344 scopus 로고
    • Various techniques used in connectionwith random digits
    • VONNEUMANN, J. 1951. Various techniques used in connectionwith random digits. Appl.Math Series 12, 36-38.
    • (1951) Appl. Math Series , vol.12 , pp. 36-38
    • Vonneumann, J.1
  • 40
    • 43849088675 scopus 로고    scopus 로고
    • Linear degree extractors and the inapproximability of max clique and chromatic number
    • Preliminary version in STOC '06
    • ZUCKERMAN, D. 2007. Linear degree extractors and the inapproximability of max clique and chromatic number. Theory Comput. 3, 1, 103-128. (Preliminary version in STOC '06).
    • (2007) Theory Comput. , vol.3 , Issue.1 , pp. 103-128
    • Zuckerman, D.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.