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Volumn 29, Issue 6, 2000, Pages 1878-1888

Complexity of the A B C problem

Author keywords

[No Author keywords available]

Indexed keywords

ENCODING (SYMBOLS); MATRIX ALGEBRA; POLYNOMIALS; PROBLEM SOLVING;

EID: 0034478926     PISSN: 00975397     EISSN: None     Source Type: Journal    
DOI: 10.1137/S0097539794276853     Document Type: Article
Times cited : (27)

References (43)
  • 1
    • 0039812564 scopus 로고
    • Algorithmic unsolvability of problems of recognition of certain properties of groups
    • in Russian
    • S. I. ADYAN, Algorithmic unsolvability of problems of recognition of certain properties of groups, Dokalady Akad. Nauk SSSR, 103 (1955), pp. 533-535 (in Russian).
    • (1955) Dokalady Akad. Nauk SSSR , vol.103 , pp. 533-535
    • Adyan, S.I.1
  • 8
    • 0342800688 scopus 로고
    • Membership testing in commutative transformation semigroups
    • M. BEAUDRY, Membership testing in commutative transformation semigroups, Inform. and Comput., 79 (1988), pp. 84-93.
    • (1988) Inform. and Comput. , vol.79 , pp. 84-93
    • Beaudry, M.1
  • 10
    • 0000326055 scopus 로고
    • Algebraic integers near the unit circle
    • P. E. BLANKSBY AND H. L. MONTGOMERY, Algebraic integers near the unit circle, Acta Arith., 18 (1971), pp. 355-369.
    • (1971) Acta Arith. , vol.18 , pp. 355-369
    • Blanksby, P.E.1    Montgomery, H.L.2
  • 11
    • 0011994346 scopus 로고
    • The word problem
    • W. W. BOONE, The word problem, Ann. of Math., 70 (1952), pp. 207-265.
    • (1952) Ann. of Math. , vol.70 , pp. 207-265
    • Boone, W.W.1
  • 12
    • 0343670986 scopus 로고
    • Computing Jordan normal forms exactly for commuting matrices in polynomial time
    • J. CAI, Computing Jordan normal forms exactly for commuting matrices in polynomial time, Internat. J. Foundations Comput. Sci., 5 (1994), pp. 293-302.
    • (1994) Internat. J. Foundations Comput. Sci. , vol.5 , pp. 293-302
    • Cai, J.1
  • 13
    • 84936760286 scopus 로고
    • Complexity of the membership problem for 2-generated commutative semigroups of rational matrices
    • Santa Fe, NM
    • J. CAI, R. LIPTON, AND Y. ZALCSTEIN, Complexity of the membership problem for 2-generated commutative semigroups of rational matrices, in Proceedings Foundation of Computer Science, Santa Fe, NM, 1994, pp. 135-142.
    • (1994) Proceedings Foundation of Computer Science , pp. 135-142
    • Cai, J.1    Lipton, R.2    Zalcstein, Y.3
  • 14
    • 0002854505 scopus 로고
    • Su di un problema combinatorio in teoria dei gruppi
    • M. CURZIO, P. LONGOBARDI, AND M. MAI, Su di un problema combinatorio in teoria dei gruppi, Atti Lincei VIII 74, (1983), pp. 136-142.
    • (1983) Atti Lincei VIII , vol.74 , pp. 136-142
    • Curzio, M.1    Longobardi, P.2    Mai, M.3
  • 16
    • 0026223216 scopus 로고
    • Complexity of Grigorchuk groups with application to cryptography
    • M. GARZON AND Y. ZALCSTEIN, Complexity of Grigorchuk groups with application to cryptography, Theoret. Comput. Sci., 88 (1991), pp. 83-98.
    • (1991) Theoret. Comput. Sci. , vol.88 , pp. 83-98
    • Garzon, M.1    Zalcstein, Y.2
  • 17
    • 51249174088 scopus 로고
    • On permutation properties in groups and semigroups
    • M. GARZON AND Y. ZALCSTEIN, On permutation properties in groups and semigroups, Semigroup Forum, 35 (1987), pp. 337-351.
    • (1987) Semigroup Forum , vol.35 , pp. 337-351
    • Garzon, M.1    Zalcstein, Y.2
  • 18
    • 0027886529 scopus 로고
    • Testing equalities of multiplicative representations in polynomial time
    • G. GE, Testing equalities of multiplicative representations in polynomial time, in Proceedings Foundation of Computer Science, 1993, pp. 422-426.
    • (1993) Proceedings Foundation of Computer Science , pp. 422-426
    • Ge, G.1
  • 20
    • 84956137775 scopus 로고
    • Degrees of growth of finitely generated groups and the theory of invariant means
    • R. I. GRIGORCHUK, Degrees of growth of finitely generated groups and the theory of invariant means, Math. USSR Izvestiya, 25 (1985), pp. 259-300.
    • (1985) Math. USSR Izvestiya , vol.25 , pp. 259-300
    • Grigorchuk, R.I.1
  • 23
    • 0013005848 scopus 로고
    • An unsolvable problem with products of matrices
    • M. KROM, An unsolvable problem with products of matrices, Math. Systems Theory, 14 (1981), pp. 335-337.
    • (1981) Math. Systems Theory , vol.14 , pp. 335-337
    • Krom, M.1
  • 24
    • 0343670970 scopus 로고
    • Solvability of the occurrence problem infinitely generated soluble groups of matrices over the field of algebraic numbers
    • L. KOPYTOV, Solvability of the occurrence problem infinitely generated soluble groups of matrices over the field of algebraic numbers, Algebra and Logic, 7 (1968), pp. 388-393.
    • (1968) Algebra and Logic , vol.7 , pp. 388-393
    • Kopytov, L.1
  • 25
    • 85046561721 scopus 로고
    • Lower bounds for natural proof systems
    • Providence, RI
    • D. KOZEN, Lower bounds for natural proof systems, in Proceedings Foundation of Computer Science, Providence, RI, 1977, pp. 254-266.
    • (1977) Proceedings Foundation of Computer Science , pp. 254-266
    • Kozen, D.1
  • 27
    • 0001047308 scopus 로고
    • Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix
    • R. KANNAN AND A. BACHEM, Polynomial algorithms for computing the Smith and Hermite normal forms of an integer matrix, SIAM J. Comput., 8 (1979), pp. 499-507.
    • (1979) SIAM J. Comput. , vol.8 , pp. 499-507
    • Kannan, R.1    Bachem, A.2
  • 28
    • 0342365736 scopus 로고
    • The orbit problem is decidable
    • Los Angeles, CA
    • R. KANNAN AND R. LIPTON, The orbit problem is decidable, in Proceedings of the 12th Symposium on the Theory of Computing, Los Angeles, CA, 1980, pp. 252-261. See also Polynomial-time algorithms for the orbit problem, JACM, 33 (1986), pp. 808-821.
    • (1980) Proceedings of the 12th Symposium on the Theory of Computing , pp. 252-261
    • Kannan, R.1    Lipton, R.2
  • 29
    • 0022793656 scopus 로고
    • Polynomial-time algorithms for the orbit problem
    • R. KANNAN AND R. LIPTON, The orbit problem is decidable, in Proceedings of the 12th Symposium on the Theory of Computing, Los Angeles, CA, 1980, pp. 252-261. See also Polynomial-time algorithms for the orbit problem, JACM, 33 (1986), pp. 808-821.
    • (1986) Jacm , vol.33 , pp. 808-821
  • 30
    • 0007513183 scopus 로고
    • Polynomial factorization and non-randomness of bits of algebraic numbers and certain transcendental numbers
    • R. KANNAN, A. K. LENSTRA, AND L. LOVÁSZ, Polynomial factorization and non-randomness of bits of algebraic numbers and certain transcendental numbers, Math. Comp., 50 (1988), pp. 235-250.
    • (1988) Math. Comp. , vol.50 , pp. 235-250
    • Kannan, R.1    Lenstra, A.K.2    Lovász, L.3
  • 31
    • 0020845921 scopus 로고
    • Integer programming with a fixed number of variables
    • H. W. LENSTRA, Integer programming with a fixed number of variables, Math. Oper. Res., 8 (1983), pp. 538-548.
    • (1983) Math. Oper. Res. , vol.8 , pp. 538-548
    • Lenstra, H.W.1
  • 32
    • 34250244723 scopus 로고
    • Factoring polynomials with rational coefficients
    • A. K. LENSTRA, H. W. LENSTRA, AND L. LOVÁSZ, Factoring polynomials with rational coefficients, Math. Ann., 261 (1982), pp. 515-534.
    • (1982) Math. Ann. , vol.261 , pp. 515-534
    • Lenstra, A.K.1    Lenstra, H.W.2    Lovász, L.3
  • 33
    • 0343670968 scopus 로고
    • personal communication, University of Massachusetts, Amherst, MA
    • S. LANDAU, personal communication, University of Massachusetts, Amherst, MA, 1994.
    • (1994)
    • Landau, S.1
  • 34
    • 84976851566 scopus 로고
    • Word problems solvable in logspace
    • R. LIPTON AND Y. ZALCSTEIN, Word problems solvable in logspace, JACM, 24 (1977), pp. 522-526.
    • (1977) JACM , vol.24 , pp. 522-526
    • Lipton, R.1    Zalcstein, Y.2
  • 36
    • 85065731689 scopus 로고
    • Computing in solvable matrix groups
    • Pittsburgh, PA
    • E. LUKS, Computing in solvable matrix groups, in Proceedings Foundation of Computer Science, Pittsburgh, PA, 1992, pp. 111-120.
    • (1992) Proceedings Foundation of Computer Science , pp. 111-120
    • Luks, E.1
  • 37
    • 0043026726 scopus 로고
    • Linear relations on algebraic groups
    • A. Baker, ed., Cambridge University Press, Cambridge, UK
    • D. W. MASSER, Linear relations on algebraic groups, in New Advances in Transcendence Theory, A. Baker, ed., Cambridge University Press, Cambridge, UK, 1988, pp. 248-262.
    • (1988) New Advances in Transcendence Theory , pp. 248-262
    • Masser, D.W.1
  • 38
    • 0009374607 scopus 로고
    • The occurrence problem for a direct product of groups
    • K. A. MIHAILOVA, The occurrence problem for a direct product of groups, Dokl. Akad. Nauk, 119 (1958), pp. 1103-1105.
    • (1958) Dokl. Akad. Nauk , vol.119 , pp. 1103-1105
    • Mihailova, K.A.1
  • 39
    • 0002996665 scopus 로고
    • On the algorithmic unsolvability of the problem of equality of words in group theory
    • in Russian
    • P. S. NOVIKOV, On the algorithmic unsolvability of the problem of equality of words in group theory, Trudy Mat. Inst. Akad. Nauk SSSR, 44 (1955), pp. 1-144 (in Russian).
    • (1955) Trudy Mat. Inst. Akad. Nauk SSSR , vol.44 , pp. 1-144
    • Novikov, P.S.1
  • 40
    • 0014751960 scopus 로고
    • Undecidability in 3 by 3 matrices
    • M. S. PATERSON, Undecidability in 3 by 3 matrices, J. Math. Phys., 49 (1970), pp. 105-107.
    • (1970) J. Math. Phys. , vol.49 , pp. 105-107
    • Paterson, M.S.1
  • 41
    • 0001161359 scopus 로고
    • Recursive unsolvability of group theoretic problems
    • M. RABIN, Recursive unsolvability of group theoretic problems, Ann. Math., 67 (1958), pp. 172-194.
    • (1958) Ann. Math. , vol.67 , pp. 172-194
    • Rabin, M.1
  • 42
    • 84968513637 scopus 로고
    • Computable algebra, general theory and theory of computable fields
    • M. RABIN, Computable algebra, general theory and theory of computable fields, Trans. Amer. Math. Soc., 95 (1960), pp. 341-360.
    • (1960) Trans. Amer. Math. Soc. , vol.95 , pp. 341-360
    • Rabin, M.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.