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Volumn 2006, Issue , 2006, Pages 363-372

Hardness of approximate two-level logic minimization and PAC learning with membership queries

Author keywords

DNF minimization; Hardness of approximation; Membership queries; Proper learning; Truth table; Two level logic minimization; Uniform distribution

Indexed keywords

ALGORITHMS; COMPUTATIONAL COMPLEXITY; COMPUTER SCIENCE; DECISION TABLES; POLYNOMIALS; PROBLEM SOLVING;

EID: 33748122867     PISSN: 07378017     EISSN: None     Source Type: Conference Proceeding    
DOI: 10.1145/1132516.1132569     Document Type: Conference Paper
Times cited : (16)

References (41)
  • 6
    • 0027308413 scopus 로고
    • Efficient probabilistically checkable proofs and applications to approximations
    • M. Bellare, S. Goldwasser, C. Lund, and A. Russell. Efficient probabilistically checkable proofs and applications to approximations. In STOC '93, pages 294-304, 1993.
    • (1993) STOC '93 , pp. 294-304
    • Bellare, M.1    Goldwasser, S.2    Lund, C.3    Russell, A.4
  • 7
    • 0029504777 scopus 로고
    • Fast learning of k-term DNF formulas with queries
    • A. Blum and S. Rudich. Fast learning of k-term DNF formulas with queries. Journal of Computer and System Sciences, 51(3):367-373, 1995.
    • (1995) Journal of Computer and System Sciences , vol.51 , Issue.3 , pp. 367-373
    • Blum, A.1    Rudich, S.2
  • 8
    • 0026453958 scopus 로고
    • Training a 3-node neural network is NP-complete
    • A. L. Blum and R. L. Rivest. Training a 3-node neural network is NP-complete. Neural Networks, 5(1):117-127, 1992.
    • (1992) Neural Networks , vol.5 , Issue.1 , pp. 117-127
    • Blum, A.L.1    Rivest, R.L.2
  • 9
    • 0028388503 scopus 로고
    • METAPRIME, an interactive fault-tree analyser
    • O. Coudert and J. Madre. METAPRIME, an Interactive Fault-Tree Analyser. IEEE Transactions on Reliability, 43(1):121-127, 1994.
    • (1994) IEEE Transactions on Reliability , vol.43 , Issue.1 , pp. 121-127
    • Coudert, O.1    Madre, J.2
  • 12
    • 27144509145 scopus 로고    scopus 로고
    • A new multilayered pep and the hardness of hypergraph vertex cover
    • I. Dinur, V. Guruswami, S. Khot, and O. Regev. A new multilayered pep and the hardness of hypergraph vertex cover. SIAM Journal of Computing, 34(5):1129-1146, 2005.
    • (2005) SIAM Journal of Computing , vol.34 , Issue.5 , pp. 1129-1146
    • Dinur, I.1    Guruswami, V.2    Khot, S.3    Regev, O.4
  • 13
    • 51249175955 scopus 로고
    • Families of finite sets in which no set is covered by the union of r others
    • P. Erdös, P. Frankl, and Z. Furedi. Families of finite sets in which no set is covered by the union of r others. Israel Journal of Mathematics, 51:79-89, 1985.
    • (1985) Israel Journal of Mathematics , vol.51 , pp. 79-89
    • Erdös, P.1    Frankl, P.2    Furedi, Z.3
  • 14
    • 0032108328 scopus 로고    scopus 로고
    • A threshold of ln n for approximating set cover
    • U. Feige. A threshold of ln n for approximating set cover. Journal of the ACM, 45(4):634-652, 1998.
    • (1998) Journal of the ACM , vol.45 , Issue.4 , pp. 634-652
    • Feige, U.1
  • 16
    • 84937652241 scopus 로고
    • A method for producing a boolean function having an arbitrary prescribed prime implicant table
    • J.F. Gimpel. A method for producing a boolean function having an arbitrary prescribed prime implicant table. IEEE Transactions on Computers, 14:485-488, 1965.
    • (1965) IEEE Transactions on Computers , vol.14 , pp. 485-488
    • Gimpel, J.F.1
  • 17
    • 0001187706 scopus 로고
    • Complexity of automaton identification from given data
    • E. A. Gold. Complexity of automaton identification from given data. Information and Control, 37:302-320, 1978.
    • (1978) Information and Control , vol.37 , pp. 302-320
    • Gold, E.A.1
  • 18
    • 33748123082 scopus 로고    scopus 로고
    • Query efficient PCPs with perfect completeness
    • Johan Håstad and Subhash Khot. Query Efficient PCPs with Perfect Completeness. Theory of Computing, 1(7):119-148, 2005.
    • (2005) Theory of Computing , vol.1 , Issue.7 , pp. 119-148
    • Håstad, J.1    Khot, S.2
  • 19
    • 0036036663 scopus 로고    scopus 로고
    • Exact learning of DNF formulas using DNF hypotheses
    • ACM, editor
    • Lisa Hellerstein and Vijay Raghavan. Exact learning of DNF formulas using DNF hypotheses. In ACM, editor, Proceedings of STOC '02, pages 465-473, 2002.
    • (2002) Proceedings of STOC '02 , pp. 465-473
    • Hellerstein, L.1    Raghavan, V.2
  • 20
    • 0031339159 scopus 로고    scopus 로고
    • An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
    • J. Jackson. An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. Journal of Computer and System Sciences, 55:414-440, 1997.
    • (1997) Journal of Computer and System Sciences , vol.55 , pp. 414-440
    • Jackson, J.1
  • 24
    • 0036168199 scopus 로고    scopus 로고
    • Routing table compaction in ternary cam
    • H. Liu. Routing table compaction in ternary cam. IEEE Micro, 22(1):58-64, 2002.
    • (2002) IEEE Micro , vol.22 , Issue.1 , pp. 58-64
    • Liu, H.1
  • 25
    • 0028514351 scopus 로고
    • On the hardness of approximating minimization problems
    • C. Lund and M. Yannakakis. On the hardness of approximating minimization problems. Journal of the ACM, 41(5):960-981, 1994.
    • (1994) Journal of the ACM , vol.41 , Issue.5 , pp. 960-981
    • Lund, C.1    Yannakakis, M.2
  • 27
    • 33845331515 scopus 로고
    • Minimization of boolean functions
    • E. L. Jr. McCluskey. Minimization of Boolean Functions. Bell Sys. Tech. Jour., 35:1417-1444, 1956.
    • (1956) Bell Sys. Tech. Jour. , vol.35 , pp. 1417-1444
    • McCluskey Jr., E.L.1
  • 30
    • 0016664545 scopus 로고
    • Boolesche minimalpolynome und überdeckungsprobleme
    • W. J. Paul. Boolesche minimalpolynome und überdeckungsprobleme. Acta Informatica, 4:321-336, 1974.
    • (1974) Acta Informatica , vol.4 , pp. 321-336
    • Paul, W.J.1
  • 31
    • 0024092215 scopus 로고
    • Computational limitations on learning from examples
    • L. Pitt and L. Valiant. Computational limitations on learning from examples. Journal of the ACM, 35 (4):965-984, 1988.
    • (1988) Journal of the ACM , vol.35 , Issue.4 , pp. 965-984
    • Pitt, L.1    Valiant, L.2
  • 32
    • 0000070975 scopus 로고
    • The problem of simplifying truth functions
    • W.V. Quine. The problem of simplifying truth functions. Americal Mathematical Monthly, 59:521-531, 1952.
    • (1952) Americal Mathematical Monthly , vol.59 , pp. 521-531
    • Quine, W.V.1
  • 33
    • 0000316190 scopus 로고
    • A way to simplify truth functions
    • W.V. Quine. A way to simplify truth functions. Americal Mathematical Monthly, 62:627-631, 1956.
    • (1956) Americal Mathematical Monthly , vol.62 , pp. 627-631
    • Quine, W.V.1
  • 34
    • 0030714232 scopus 로고    scopus 로고
    • A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP
    • R. Raz and S. Safra. A sub-constant error-probability low-degree test, and a sub-constant error-probability PCP characterization of NP. In Proceedings of STOC '97, pages 475-484, 1997.
    • (1997) Proceedings of STOC '97 , pp. 475-484
    • Raz, R.1    Safra, S.2
  • 36
    • 0034826228 scopus 로고    scopus 로고
    • Non-approximability results for optimization problems on bounded degree instances
    • L. Trevisan. Non-approximability results for optimization problems on bounded degree instances. In Proceedings of STOC '01, pages 453-461, 2001.
    • (2001) Proceedings of STOC '01 , pp. 453-461
    • Trevisan, L.1
  • 37
    • 0035734260 scopus 로고    scopus 로고
    • The minimum equivalent DNF problem and shortest implicants
    • C. Umans. The minimum equivalent DNF problem and shortest implicants. J. Comput. Syst. Sci., 63(4):597-611, 2001.
    • (2001) J. Comput. Syst. Sci. , vol.63 , Issue.4 , pp. 597-611
    • Umans, C.1
  • 38
    • 33748113311 scopus 로고    scopus 로고
    • Complexity of two-level logic minimization
    • UC Berkeley, October
    • C. Umans, T. Villa, and A. L. Sangiovanni-Vincentelli. Complexity of two-level logic minimization. Technical Report UCB/ERL M04/45, UC Berkeley, October 2004.
    • (2004) Technical Report , vol.UCB-ERL M04-45
    • Umans, C.1    Villa, T.2    Sangiovanni-Vincentelli, A.L.3
  • 40
    • 0021518106 scopus 로고
    • A theory of the learnable
    • L. Valiant. A theory of the learnable. Communications of the ACM, 27(11):1134-1142, 1984.
    • (1984) Communications of the ACM , vol.27 , Issue.11 , pp. 1134-1142
    • Valiant, L.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.