메뉴 건너뛰기




Volumn 176, Issue 3, 2012, Pages 1483-1544

2-Source dispersers for n°(1) entropy, and ramsey graphs beating the frankl-wilson construction

Author keywords

[No Author keywords available]

Indexed keywords


EID: 84872472857     PISSN: 0003486X     EISSN: None     Source Type: Journal    
DOI: 10.4007/annals.2012.176.3.3     Document Type: Article
Times cited : (55)

References (27)
  • 1
    • 0032411859 scopus 로고    scopus 로고
    • The Shannon capacity of a union
    • MR 1721946. Zbl 0921.05039
    • N. Alon, The Shannon capacity of a union, Combinatorica 18 (1998), 301-310. MR 1721946. Zbl 0921.05039. http://dx.doi.org/10.1007/PL00009824.
    • (1998) Combinatorica , vol.18 , pp. 301-310
    • Alon, N.1
  • 2
    • 84858943111 scopus 로고    scopus 로고
    • A simple explicit construction of an n~o(log n)-Ramsey graph
    • arXiv math.CO/0601651
    • õ(log n)-Ramsey graph, 2006, Tech. report. arXiv math.CO/0601651.
    • (2006) Tech. report.
    • Barak, B.1
  • 3
    • 34247566037 scopus 로고    scopus 로고
    • Extracting randomness using few independent sources
    • preliminary version in FOCS 2004, MR 2272272. Zbl 1127.68030
    • B. Barak, R. Impagliazzo, and A. Wigderson, Extracting randomness using few independent sources, SIAM J. Comput. 36 (2006), 1095- 1118, preliminary version in FOCS 2004. MR 2272272. Zbl 1127.68030. http://dx.doi.org/10.1137/S0097539705447141.
    • (2006) SIAM J. Comput. , vol.36
    • Barak, B.1    Impagliazzo, R.2    Wigderson, A.3
  • 4
    • 77952022169 scopus 로고    scopus 로고
    • Simulating independence: New constructions of condensers
    • preliminary version in STOC 2005, MR 2677118. Zbl 1192.68468
    • B. Barak, G. Kindler, R. Shaltiel, B. Sudakov, and A. Wigderson, Simulating independence: New constructions of condensers, Ramsey graphs, dispersers, and extractors, J. ACM 57 (2010), 52pp, preliminary version in STOC 2005. MR 2677118. Zbl 1192.68468. http: //dx.doi.org/10.1145/1734213.1734214.
    • (2010) Ramsey graphs, dispersers, and extractors, J. ACM , vol.57 , pp. 52
    • Barak, B.1    Kindler, G.2    Shaltiel, R.3    Sudakov, B.4    Wigderson, A.5
  • 5
    • 33746365070 scopus 로고    scopus 로고
    • More on the sum-product phenomenon in prime fields and its applications
    • MR 2172328. Zbl 1173.11310
    • J. Bourgain, More on the sum-product phenomenon in prime fields and its applications, Int. J. Number Theory 1 (2005), 1-32. MR 2172328. Zbl 1173.11310. http://dx.doi.org/10.1142/S1793042105000108.
    • (2005) Int. J. Number Theory , vol.1 , pp. 1-32
    • Bourgain, J.1
  • 6
    • 2442427378 scopus 로고    scopus 로고
    • A sum-product estimate in finite fields, and applications
    • MR 2053599. Zbl 1145.11306
    • J. Bourgain, N. Katz, and T. Tao, A sum-product estimate in finite fields, and applications, Geom. Funct. Anal. 14 (2004), 27-57. MR 2053599. Zbl 1145.11306. http://dx.doi.org/10.1007/s00039-004-0451-1.
    • (2004) Geom. Funct. Anal. , vol.14 , pp. 27-57
    • Bourgain, J.1    Katz, N.2    Tao, T.3
  • 8
    • 0023985259 scopus 로고
    • Unbiased bits from sources of weak randomness and probabilistic communication complexity
    • MR 0935339. Zbl 0644.94008
    • B. Chor and O. Goldreich, Unbiased bits from sources of weak randomness and probabilistic communication complexity, SIAM J. Comput. 17 (1988), 230-261. MR 0935339. Zbl 0644.94008. http://dx.doi.org/10.1109/SFCS.1985.62.
    • (1988) SIAM J. Comput. , vol.17 , pp. 230-261
    • Chor, B.1    Goldreich, O.2
  • 10
    • 51249185135 scopus 로고
    • Intersection theorems with geometric consequences
    • MR 0647986. Zbl 0498. 05048
    • P. Frankl and R. M. Wilson, Intersection theorems with geometric consequences, Combinatorica 1 (1981), 357-368. MR 0647986. Zbl 0498. 05048. http://dx.doi.org/10.1007/BF02579457.
    • (1981) Combinatorica , vol.1 , pp. 357-368
    • Frankl, P.1    Wilson, R.M.2
  • 12
    • 0011229016 scopus 로고    scopus 로고
    • Low rank co-diagonal matrices and Ramsey graphs
    • Research Paper 15,MR 1756284. Zbl 0939.05060, Available at
    • V. Grolmusz, Low rank co-diagonal matrices and Ramsey graphs, Elec- tron. J. Combin. 7 (2000), Research Paper 15, 7 pp. MR 1756284. Zbl 0939.05060. Available at http://www.combinatorics.org/ojs/index.php/eljc/article/view/v7i1r15.
    • (2000) Electron. J. Combin. , vol.7 , pp. 7
    • Grolmusz, V.1
  • 13
    • 4544262873 scopus 로고    scopus 로고
    • Better extractors for better codes?
    • ACM, New York, MR 2121629. Zbl 1192.68363
    • V. Guruswami, Better extractors for better codes?, in Proceedings of the 36th Annual ACM Symposium on Theory of Computing, ACM, New York, 2004, pp. 436-444. MR 2121629. Zbl 1192.68363. http://dx.doi.org/10.1145/1007352.1007422.
    • (2004) Proceedings of the 36th Annual ACM Symposium on Theory of Computing , pp. 436-444
    • Guruswami, V.1
  • 15
    • 0032142025 scopus 로고    scopus 로고
    • On data structures and asymmetric communication complexity
    • MR 1649806. Zbl 0920.68042
    • P. B. Miltersen, N. Nisan, S. Safra, and A. Wigderson, On data structures and asymmetric communication complexity, J. Comput. System Sci. 57 (1998), 37-49. MR 1649806. Zbl 0920.68042. http://dx.doi.org/10.1006/jcss.1998.1577.
    • (1998) J. Comput. System Sci. , vol.57 , pp. 37-49
    • Miltersen, P.B.1    Nisan, N.2    Safra, S.3    Wigderson, A.4
  • 16
    • 33750330247 scopus 로고    scopus 로고
    • Pseudorandom sets and explicit constructions of Ramsey graphs, in Complexity of Computations and Proofs
    • MR 2131412. Zbl 1074.05088
    • P. Pudlák and V. Rödl, Pseudorandom sets and explicit constructions of Ramsey graphs, in Complexity of Computations and Proofs, Quad. Mat. 13, Dept. Math., Seconda Univ. Napoli, Caserta, 2004, pp. 327-346. MR 2131412. Zbl 1074.05088.
    • (2004) Quad. Mat. 13, Dept. Math., Seconda Univ. Napoli, Caserta , pp. 327-346
    • Pudlák, P.1    Rödl, V.2
  • 17
    • 84960601644 scopus 로고
    • On a problem of formal logic
    • MR 1576401. JFM 55.0032.04.
    • F. P. Ramsey, On a problem of formal logic, Proc. London Math. Soc. S2-30 (1930), 264-286. MR 1576401. JFM 55.0032.04. http://dx.doi.org/10.1112/plms/s2-30.1.264.
    • (1930) Proc. London Math. Soc. S2-30 , pp. 264-286
    • Ramsey, F.P.1
  • 18
    • 67650164537 scopus 로고    scopus 로고
    • Extractors for a constant number of polynomially small minentropy independent sources
    • preliminary version in STOC 2006
    • A. Rao, Extractors for a constant number of polynomially small minentropy independent sources, SIAM J. Comput. 39 (2009), 168-194, preliminary version in STOC 2006. http://dx.doi.org/10.1137/060671218.
    • (2009) SIAM J. Comput. , vol.39 , pp. 168-194
    • Rao, A.1
  • 19
  • 20
    • 0038309373 scopus 로고    scopus 로고
    • Extracting all the randomness and reducing the error in Trevisan's extractors
    • MR 1946290. Zbl 1020.68029
    • R. Raz, O. Reingold, and S. Vadhan, Extracting all the randomness and reducing the error in Trevisan's extractors, J. Comput. System Sci. 65 (2002), 97-128. MR 1946290. Zbl 1020.68029. http://dx.doi.org/10.1006/jcss.2002.1824.
    • (2002) J. Comput. System Sci. , vol.65 , pp. 97-128
    • Raz, R.1    Reingold, O.2    Vadhan, S.3
  • 21
    • 0034503771 scopus 로고    scopus 로고
    • Extracting randomness via repeated condensing, in 41st Annual Symposium on Founda- tions of Computer Science (Redondo Beach, CA, 2000)
    • MR 1931801
    • O. Reingold, R. Shaltiel, and A. Wigderson, Extracting randomness via repeated condensing, in 41st Annual Symposium on Founda- tions of Computer Science (Redondo Beach, CA, 2000), IEEE Comput. Soc. Press, Los Alamitos, CA, 2000, pp. 22-31. MR 1931801. http://dx.doi.org/10.1109/SFCS.2000.892008.
    • (2000) IEEE Comput. Soc. Press, Los Alamitos, CA , pp. 22-31
    • Reingold, O.1    Shaltiel, R.2    Wigderson, A.3
  • 22
    • 0021469810 scopus 로고
    • Generating quasi-random sequences from semi-random sources
    • MR 0864080. Zbl 0612.94004
    • M. Sántha and U. V. Vazirani, Generating quasi-random sequences from semi-random sources, J. Comput. System Sci. 33 (1986), 75-87. MR 0864080. Zbl 0612.94004. http://dx.doi.org/10.1016/0022-0000(86)90044-9.
    • (1986) J. Comput. System Sci. , vol.33 , pp. 75-87
    • Sántha, M.1    Vazirani, U.V.2
  • 23
    • 0012579059 scopus 로고    scopus 로고
    • Recent developments in explicit constructions of extractors
    • MR 1920329. Zbl 1051.68070
    • R. Shaltiel, Recent developments in explicit constructions of extractors, Bull. Eur. Assoc. Theor. Comput. Sci. EATCS (2002), 67-95. MR 1920329. Zbl 1051.68070.
    • (2002) Bull. Eur. Assoc. Theor. Comput. Sci. EATCS , pp. 67-95
    • Shaltiel, R.1
  • 24
    • 10644226110 scopus 로고    scopus 로고
    • Extractor codes
    • MR 2103480
    • A. Ta-Shma and D. Zuckerman, Extractor codes, IEEE Trans. Inform. Theory 50 (2004), 3015-3025. MR 2103480. http://dx.doi.org/10.1109/TIT.2004.838377.
    • (2004) IEEE Trans. Inform. Theory , vol.50 , pp. 3015-3025
    • Ta-Shma, A.1    Zuckerman, D.2
  • 25
    • 0005314594 scopus 로고    scopus 로고
    • Extractors and pseudorandom generators
    • MR 2144932. Zbl 1127.68403
    • L. Trevisan, Extractors and pseudorandom generators, J. ACM 48 (2001), 860-879. MR 2144932. Zbl 1127.68403. http://dx.doi.org/10.1145/502090.502099.
    • (2001) J. ACM , vol.48 , pp. 860-879
    • Trevisan, L.1
  • 26
    • 0021901103 scopus 로고
    • Towards a strong communication complexity theory or generating quasi-random sequences from two communicating slightlyrandom sources (extended abstract)
    • U. Vazirani, Towards a strong communication complexity theory or generating quasi-random sequences from two communicating slightlyrandom sources (extended abstract), in Proceedings of the 17th An- nual ACM Symposium on Theory of Computing, 1985, pp. 366-378. http://dx.doi.org/10.1145/22145.22186.
    • (1985) Proceedings of the 17th An- nual ACM Symposium on Theory of Computing , pp. 366-378
    • Vazirani, U.1
  • 27
    • 0040707391 scopus 로고    scopus 로고
    • Expanders that beat the eigenvalue bound: explicit construction and applications
    • MR 1722214. Zbl 0929.05075
    • A. Wigderson and D. Zuckerman, Expanders that beat the eigenvalue bound: explicit construction and applications, Combinatorica 19 (1999), 125-138. MR 1722214. Zbl 0929.05075. http://dx.doi.org/10.1007/s004930050049.
    • (1999) Combinatorica , vol.19 , pp. 125-138
    • Wigderson, A.1    Zuckerman, D.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.