메뉴 건너뛰기




Volumn 47, Issue 3, 2000, Pages 506-530

Learning functions represented as multiplicity automata

Author keywords

Computational learning; DNF; Learning disjoint; Learning polynomials; Multiplicity automata

Indexed keywords

LEARNING FUNCTIONS; LEARNING POLYNOMIALS; MULTIPLICITY AUTOMATA;

EID: 2342490453     PISSN: 00045411     EISSN: None     Source Type: Journal    
DOI: 10.1145/337244.337257     Document Type: Article
Times cited : (107)

References (60)
  • 2
    • 0026962977 scopus 로고
    • Exact learning of read-k disjoint DNF and not-so-disjoint DNF
    • AIZENSTEIN, H., AND PITT, L. 1992. Exact learning of read-k disjoint DNF and not-so-disjoint DNF. In Proceedings of 5th Annual ACM Workshop on Computational Learning Theory (Pittsburgh, Pa., July 27-29). ACM, New York, pp. 71-76.
    • (1992) In Proceedings of , vol.5 , pp. 71-76
    • Aizenstein, H.1    Pitt, L.2
  • 3
    • 0013450466 scopus 로고
    • Learning k-term DNF formulas using queries and counterexamples
    • ANGLUIN, D. 1987a. Learning k-term DNF formulas using queries and counterexamples. Tech. Rep. YALEU/DCS/RR-559. Dept. Computer Science; Yale University.
    • (1987) Tech. Rep. YALEU/DCS/RR , vol.559
    • Angluin, D.1
  • 4
    • 0023453626 scopus 로고
    • Learning regular sets from queries and counterexamples
    • ANGLUIN, D. 1987b. Learning regular sets from queries and counterexamples. Inf. Comput. 75, 87-106.
    • (1987) Inf. Comput. , vol.75 , pp. 87-106
    • Angluin, D.1
  • 5
    • 0000710299 scopus 로고
    • Queries and concept learning
    • ANGLUIN, D. 1988. Queries and concept learning. Mach. Learn. 2, 4, 319-342.
    • (1988) Mach. Learn. , vol.2 , pp. 319-342
    • Angluin, D.1
  • 6
    • 0027341861 scopus 로고
    • Learning read-once formulas with queries
    • ANGLUIN, D., HELLERSTEIN, L., AND KARPINSKI, M. 1993. Learning read-once formulas with queries. J. ACM 40, 185-210.
    • (1993) J. ACM , vol.40 , pp. 185-210
    • Angluin, D.1    Hellerstein, L.2    Karpinski, M.3
  • 7
    • 0027883936 scopus 로고
    • On-line learning of rectangles in noisy environments
    • AUER, P. 1993. On-line learning of rectangles in noisy environments. In Proceedings of 6th Annual ACM Conference on Computational Learning Theory, (Santa Cruz, Calif., July 26-28). ACM, New York, pp. 253-261.
    • (1993) In Proceedings of , vol.6 , pp. 253-261
    • Auer, P.1
  • 8
    • 0030402331 scopus 로고    scopus 로고
    • On the applications of multiplicity automata in learning
    • BEIMEL, A., BERGADANO, F., BSHOUTY, N. H., KUSHILEVITZ, E., AND VARRICCHIO, S. 1996. On the applications of multiplicity automata in learning. In Proceedings of the 37th Annual IEEE Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 349-358.
    • (1996) In Proceedings of the , vol.37 , pp. 349-358
    • Beimel, A.1    Bergadano, F.2    Bshouty, N.H.3    Kushilevitz, E.4    Varricchio, S.5
  • 9
    • 2342543752 scopus 로고    scopus 로고
    • Learning boxes in high dimension
    • BEIMEL, A., AND KUSHILEVITZ, E. 1998. Learning boxes in high dimension. Algorithmica, 22, 76-90.
    • (1998) Algorithmica , vol.22 , pp. 76-90
    • Beimel, A.1    Kushilevitz, E.2
  • 10
    • 84898974734 scopus 로고
    • A deterministic algorithm for sparse multivariate polynomial interpolation
    • BEN-OR, M., AND TIWARI, P. 1988. A deterministic algorithm for sparse multivariate polynomial interpolation. In Proceedings of the 20th Annual ACM Symposium on Theory of Computing (Chicago, 111., May 2-4). ACM, New York, pp. 301-309.
    • (1988) In Proceedings of the , vol.20 , pp. 301-309
    • Ben-Or, M.1    Tiwari, P.2
  • 11
    • 0029725149 scopus 로고    scopus 로고
    • Learning sat-k-DNF formulas from membership queries
    • BERGADANO, F., CATALANO, D., AND VARRICCHIO, S. 1996. Learning sat-k-DNF formulas from membership queries. In Proceedings of the 28th Annual ACM Symposium on the Theory of Computing (Philadelphia, Pa., May 22-24). ACM, New York, pp. 126-130.
    • (1996) In Proceedings of the , vol.28 , pp. 126-130
    • Bergadano, F.1    Catalano, D.2    Varricchio, S.3
  • 12
    • 0012743043 scopus 로고    scopus 로고
    • Learning behaviors of automata from multiplicity and equivalence queries
    • BERGADANO, F., AND VARRICCHIO, S. 1996a. Learning behaviors of automata from multiplicity and equivalence queries. SIAM J. Comput. 25, 6, 1268-1280.
    • (1996) SIAM J. Comput. , vol.25 , pp. 1268-1280
    • Bergadano, F.1    Varricchio, S.2
  • 15
    • 84943226623 scopus 로고
    • On learning read-k-satisfy-j DNF
    • SLUM, A., KHARDON, R., KUSHILEVITZ, E., PITT, L., AND ROTH, D. 1994. On learning read-k-satisfy-j DNF. In Proceedings of 7th Annual ACM Conference on Computational Learning Theory (New Brunswick, N.J., July 12-15). ACM, New York, pp. 110-117.
    • (1994) In Proceedings of , vol.7 , pp. 110-117
    • Slum, A.1    Khardon, R.2    Kushilevitz, E.3    Pitt, L.4    Roth, D.5
  • 16
    • 0029504777 scopus 로고
    • Fast learning of k-term DNF formulas with queries
    • BLUM, A., AND RUDICH, S. 1995. Fast learning of k-term DNF formulas with queries. J. Comput. Syst. Sci. 51, 3, 367-373.
    • (1995) J. Comput. Syst. Sci. , vol.51 , pp. 367-373
    • Blum, A.1    Rudich, S.2
  • 18
    • 58149319164 scopus 로고
    • Exact learning via the monotone theory
    • BSHOUTY, N. H. 1995a. Exact learning via the monotone theory. Inf. Comput. 123, 1, 146-153.
    • (1995) Inf. Comput. , vol.123 , pp. 146-153
    • Bshouty, N.H.1
  • 19
    • 4243172954 scopus 로고
    • A note on learning multivariate polynomials under the uniform distribution
    • BSHOUTY, N. H. 1995b. A note on learning multivariate polynomials under the uniform distribution. In Proceedings of 8th Annual. ACM Conference on Computational Learning Theory (Santa Cruz, Calif., July 5-8). ACM, New York, pp. 79-82.
    • (1995) In Proceedings of , vol.8 , pp. 79-82
    • Bshouty, N.H.1
  • 20
    • 0039015431 scopus 로고    scopus 로고
    • Simple learning algorithms using divide and conquer
    • BSHOUTY, N. H. 1997. Simple learning algorithms using divide and conquer. Comput. Complex. 6, 174-194.
    • (1997) Comput. Complex. , vol.6 , pp. 174-194
    • Bshouty, N.H.1
  • 21
    • 0029487221 scopus 로고
    • Simple learning algorithms for decision trees and multivariate polynomials
    • BSHOUTY, N. H., AND MANSOUR, Y. 1995. Simple learning algorithms for decision trees and multivariate polynomials. In Proceedings of the 36th Annual IEEE Symposium on Foundations of Computer Science. IEEE, New York, pp. 304-311.
    • (1995) In Proceedings of the , vol.36 , pp. 304-311
    • Bshouty, N.H.1    Mansour, Y.2
  • 22
    • 4243120064 scopus 로고    scopus 로고
    • Learning matrix functions over rings
    • BSHOUTY, N. H., TAMON, C., AND WILSON, D. K. 1998. Learning matrix functions over rings. Algorithmica 22, 91-111.
    • (1998) Algorithmica , vol.22 , pp. 91-111
    • Bshouty, N.H.1    Tamon, C.2    Wilson, D.K.3
  • 23
    • 0015018335 scopus 로고
    • Realization by stochastic finite automaton
    • CARLYLE, J. W., AND PAZ, A. 1971. Realization by stochastic finite automaton. J. Comput. Syst. Sci. 5, 26-40.
    • (1971) J. Comput. Syst. Sci. , vol.5 , pp. 26-40
    • Carlyle, J.W.1    Paz, A.2
  • 24
    • 0026966650 scopus 로고
    • On-line learning of rectangles
    • CHEN, Z., AND MAASS, W. 1992. On-line learning of rectangles. In Proceedings of 5th Annual ACM Workshop on Computational Learning Theory, (Pittsburgh, Pa., July 27-29). ACM, New York, pp. 16-28.
    • (1992) In Proceedings of , vol.5 , pp. 16-28
    • Chen, Z.1    Maass, W.2
  • 25
    • 0026189928 scopus 로고
    • On zero-testing and interpolation of k-sparse multivariate polynomials over finite fields
    • CLAUSEN, M., DRESS, A., GRABMEIER, J., AND KARPINSKI, M. 1991. On zero-testing and interpolation of k-sparse multivariate polynomials over finite fields. Theoret. Comput. Sci. 84, 2, 151-164.
    • (1991) Theoret. Comput. Sci. , vol.84 , pp. 151-164
    • Clausen, M.1    Dress, A.2    Grabmeier, J.3    Karpinski, M.4
  • 28
    • 0000692177 scopus 로고
    • Matrices de Hankel
    • FLIESS, M. 1974. Matrices de Hankel. J. Math. Pures Appl., 53, 197-222. (Erratum in vol. 54, 1975.)
    • (1974) J. Math. Pures Appl. , vol.53 , pp. 197-222
    • Fliess, M.1
  • 29
    • 85030051641 scopus 로고
    • Learning unions of boxes with membership and equivalence queries
    • GOLDBERG, P. W., GOLDMAN, S. A., AND MATHIAS, H. D. 1994. Learning unions of boxes with membership and equivalence queries. In Proceedings of 7th Annual ACM Conference on Computational Learning Theory (New Brunswick, N.J., July 12-15) ACM, New York, pp. 148-207.
    • (1994) In Proceedings of , vol.7 , pp. 148-207
    • Goldberg, P.W.1    Goldman, S.A.2    Mathias, H.D.3
  • 30
    • 0025694134 scopus 로고
    • Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields
    • GRIGORIEV, D. Y., KARPINSKI, M., AND SINGER, M. F. 1990. Fast parallel algorithms for sparse multivariate polynomial interpolation over finite fields. SIAM J. Comput. 19, 6, 1059-1063.
    • (1990) SIAM J. Comput. , vol.19 , pp. 1059-1063
    • Grigoriev, D.Y.1    Karpinski, M.2    Singer, M.F.3
  • 32
    • 0040597488 scopus 로고    scopus 로고
    • Interpolation of sparse multivariate polynomials over large finite fields with applications
    • HUANG, M. A., AND RAO, A. J. 1996. Interpolation of sparse multivariate polynomials over large finite fields with applications. In Proceedings of the 7th Annual ACM-SIAM Symposium on Discrete Algorithms. ACM, New York, pp. 508-517.
    • (1996) In Proceedings of the , vol.7 , pp. 508-517
    • Huang, M.A.1    Rao, A.J.2
  • 33
    • 0031339159 scopus 로고    scopus 로고
    • An efficient membership-query algorithm for learning DNF with respect to the uniform distribution
    • JACKSON, J. C. 1997. An efficient membership-query algorithm for learning DNF with respect to the uniform distribution. J. Comput. Syst. Sci. 55, 3, 414-440.
    • (1997) J. Comput. Syst. Sci. , vol.55 , pp. 414-440
    • Jackson, J.C.1
  • 34
    • 0028324717 scopus 로고
    • Cryptographic limitations on learning Boolean formulae and finite automata
    • KEARNS, M. J., AND VALIANT, L. G. 1994. Cryptographic limitations on learning Boolean formulae and finite automata. J. ACM 41, 1 (Jan.), 67-95.
    • (1994) J. ACM , vol.41 , pp. 67-95
    • Kearns, M.J.1    Valiant, L.G.2
  • 36
    • 0027187277 scopus 로고
    • Cryptographic hardness of distribution-specific learning
    • KHARITONOY, M. 1993. Cryptographic hardness of distribution-specific learning. In Proceedings of the 25th Annual ACM Symposium on the Theory of Computing (San Diego, Calif., May 16-18). ACM, New York, pp. 372-381.
    • (1993) In Proceedings of the , vol.25 , pp. 372-381
    • Kharitonoy, M.1
  • 37
    • 0003294665 scopus 로고    scopus 로고
    • The Art of Computer Programming
    • KNUTH, D. E. 1998. The Art of Computer Programming. Vol. 2: Seminumerical Algorithms. Addison-Wesley, Reading, Mass.
    • (1998) Vol. , vol.2
    • Knuth, D.E.1
  • 38
    • 0001030750 scopus 로고    scopus 로고
    • A simple algorithm for learning O(log n)-term DNF
    • KUSHILEVITZ, E. 1997. A simple algorithm for learning O(log n)-term DNF. In Inform. Process. Lett. 61, 6, 289-292.
    • (1997) In Inform. Process. Lett. , vol.61 , pp. 289-292
    • Kushilevitz, E.1
  • 39
    • 0027869083 scopus 로고
    • Learning decision trees using the Fourier spectrum
    • KUSHILEVITZ, E., AND MANSOUR, Y. 1993. Learning decision trees using the Fourier spectrum. SIAM J. Comput. 22, 6, 1331-1348.
    • (1993) SIAM J. Comput. , vol.22 , pp. 1331-1348
    • Kushilevitz, E.1    Mansour, Y.2
  • 41
    • 0026995322 scopus 로고
    • Random DFA's can be approximately learned from sparse uniform examples
    • LANG, K. J. 1992. Random DFA's can be approximately learned from sparse uniform examples. In Proceedings of 5th Annual ACM Workshop on Computational Learning Theory (Pittsburgh, Pa., July 27-29). ACM, New York, pp. 45-52.
    • (1992) In Proceedings of , vol.5 , pp. 45-52
    • Lang, K.J.1
  • 43
    • 0024768667 scopus 로고
    • On the complexity of learning from counterexamples
    • MAASS, W., AND TURAN, G. 1989. On the complexity of learning from counterexamples. In Proceedings of the 30th Animal IEEE Symposium on Foundations of Computer Science. IEEE Computer Society Press, Los Alamitos, Calif., pp. 262-273.
    • (1989) In Proceedings of the , vol.30 , pp. 262-273
    • Maass, W.1    Turan, G.2
  • 44
    • 0028384661 scopus 로고
    • Algorithms and lower bounds for on-line learning of geometrical concepts
    • MAASS, W., AND TURAN, G. 1994. Algorithms and lower bounds for on-line learning of geometrical concepts. Mach. Learning 14, 251-269.
    • (1994) Mach. Learning , vol.14 , pp. 251-269
    • Maass, W.1    Turan, G.2
  • 45
    • 0001784922 scopus 로고    scopus 로고
    • Efficient learning with virtual threshold gates
    • MAASS, W., AND WARMUTH, M. K. 1998. Efficient learning with virtual threshold gates. Inf. Comput. 141, 1, 66-83.
    • (1998) Inf. Comput. , vol.141 , pp. 66-83
    • Maass, W.1    Warmuth, M.K.2
  • 46
    • 0028529868 scopus 로고
    • A polynomial time learning algorithm for recognizable series
    • OHNISHI, H., SEKI, H., AND KASAMI, T. 1994. A polynomial time learning algorithm for recognizable series. IEICE Trans. Inf. Syst. E77-D, (10) (5), 1077-1085.
    • (1994) IEICE Trans. Inf. Syst. e , vol.77 , Issue.10 , pp. 1077-1085
    • Ohnishi, H.1    Seki, H.2    Kasami, T.3
  • 47
    • 0013097771 scopus 로고
    • Read-twice DNF formulas are properly learnable
    • PILLAIPAKKAMNATT, K., AND RAGHAVAN, V. 1995. Read-twice DNF formulas are properly learnable. Inf. Comput. 122, 2, 236-267.
    • (1995) Inf. Comput. , vol.122 , pp. 236-267
    • Pillaipakkamnatt, K.1    Raghavan, V.2
  • 48
    • 33744584654 scopus 로고
    • Induction of decision trees
    • QUINLAN, J. R. 1986. Induction of decision trees. Mach. Learn. 1, 81-106.
    • (1986) Mach. Learn. , vol.1 , pp. 81-106
    • Quinlan, J.R.1
  • 49
    • 0005685575 scopus 로고
    • C4.5: Programs for machine learning
    • QUINLAN, J. R. 1993. C4.5: Programs for machine learning. Morgan-Kaufmann.
    • (1993) Morgan-Kaufmann.
    • Quinlan, J.R.1
  • 50
    • 0001349185 scopus 로고
    • Inference of finite automata using homing sequences
    • RIVEST, R. L., AND SCHAPIRE, R. E. 1993. Inference of finite automata using homing sequences. Inf. Comput. 103, 299-347.
    • (1993) Inf. Comput. , vol.103 , pp. 299-347
    • Rivest, R.L.1    Schapire, R.E.2
  • 51
    • 0026136717 scopus 로고
    • Interpolation and approximation of sparse multivariate polynomials over GF(2)
    • ROTH, R. M., AND BENEDEK, G. M. 1991. Interpolation and approximation of sparse multivariate polynomials over GF(2). SIAM J. Comput. 20, 2, 291-314.
    • (1991) SIAM J. Comput. , vol.20 , pp. 291-314
    • Roth, R.M.1    Benedek, G.M.2
  • 52
    • 0030126034 scopus 로고    scopus 로고
    • Learning sparse multivariate polynomials over a field with queries and counterexamples
    • SCHAPIRE, R. E., AND SELLIE, L. M. 1996. Learning sparse multivariate polynomials over a field with queries and counterexamples. J. Comput. Syst. Sci. 52, 2, 201-213.
    • (1996) J. Comput. Syst. Sci. , vol.52 , pp. 201-213
    • Schapire, R.E.1    Sellie, L.M.2
  • 53
    • 84976779342 scopus 로고
    • Fast probabilistic algorithms for verification of polynomial identities
    • SCHWARTZ, J. T. 1980. Fast probabilistic algorithms for verification of polynomial identities. J. ACM 27, 701-717.
    • (1980) J. ACM , vol.27 , pp. 701-717
    • Schwartz, J.T.1
  • 54
    • 50549180615 scopus 로고
    • On the definition of a family of automata
    • SHÜTZENBERGER, M. P. 1961. On the definition of a family of automata. Inf. Control 4, 245-270.
    • (1961) Inf. Control , vol.4 , pp. 245-270
    • Shützenberger, M.P.1
  • 56
    • 0021518106 scopus 로고
    • A theory of the learnable
    • VALIANT, L. G. 1984. A theory of the learnable. Commun. ACM 27, 11 (Nov.), 1134-1142.
    • (1984) Commun. ACM , vol.27 , pp. 1134-1142
    • Valiant, L.G.1
  • 59
    • 0000595168 scopus 로고
    • Interpolating polynomials from their values
    • ZIPPEL, R. E. 1990. Interpolating polynomials from their values. J. Symbolic Comput. 9, 375-403.
    • (1990) J. Symbolic Comput. , vol.9 , pp. 375-403
    • Zippel, R.E.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.