메뉴 건너뛰기




Volumn 1705 LNAI, Issue , 1999, Pages 13-32

On the complexity of counting the Hilbert basis of a linear Diophantine system

Author keywords

[No Author keywords available]

Indexed keywords

DIOPHANTINE SYSTEM; HILBERT BASIS; HOMOGENEOUS SYSTEM; LINEAR DIOPHANTINE EQUATIONS; LOWER AND UPPER BOUNDS;

EID: 0006984691     PISSN: 03029743     EISSN: 16113349     Source Type: Book Series    
DOI: 10.1007/3-540-48242-3_2     Document Type: Conference Paper
Times cited : (8)

References (38)
  • 1
    • 0025625499 scopus 로고
    • A new AC unification algorithm with a new algorithm for solving Diophantine equations
    • June
    • A. Boudet, E. Contejean, and H. Devie. A new AC unification algorithm with a new algorithm for solving Diophantine equations. In Proceedings 5th Lies, Philadelphia (PA, USA), pages 289-299, June 1990.
    • (1990) Proceedings 5th Lies, Philadelphia (PA, USA) , pp. 289-299
    • Boudet, A.1    Contejean, E.2    Devie, H.3
  • 4
    • 34250081879 scopus 로고
    • Competing for the AC-unification race
    • A. Boudet. Competing for the AC-unification race. Journal of Automated Reasoning, 11(2):185-212, 1993.
    • (1993) Journal of Automated Reasoning , vol.11 , Issue.2 , pp. 185-212
    • Boudet, A.1
  • 5
    • 0001113391 scopus 로고
    • An efficient incremental algorithm for solving systems of linear Diophantine equations
    • E. Contejean and H. Devie. An efficient incremental algorithm for solving systems of linear Diophantine equations. Information and Computation, 113(1):143-172, 1994.
    • (1994) Information and Computation , vol.113 , Issue.1 , pp. 143-172
    • Contejean, E.1    Devie, H.2
  • 6
    • 85015722904 scopus 로고
    • Efficient solution of linear Diophantine equations
    • M. Clausen and A. Fortenbacher. Efficient solution of linear Diophantine equations. Journal of Symbolic Computation, 8(1-2) :201-216, 1989.
    • (1989) Journal of Symbolic Computation , vol.8 , Issue.1-2 , pp. 201-216
    • Clausen, M.1    Fortenbacher, A.2
  • 7
    • 84886267807 scopus 로고    scopus 로고
    • On the complexity of recognizing the Hilbert basis of a Unear Diophantine system
    • L. Pacholski, editor, Springer-Verlag, September
    • A. Durand, M. Hermann, and L. Jubzin. On the complexity of recognizing the Hilbert basis of a Unear Diophantine system. In L. Pacholski, editor. Proceedings 24th MFCS, Szklarska Poreba (Poland), LNCS, Springer-Verlag, September 1999.
    • (1999) Proceedings 24th MFCS, Szklarska Poreba (Poland), LNCS
    • Durand, A.1    Hermann, M.2    Jubzin, L.3
  • 9
    • 85012911905 scopus 로고
    • Solving systems of linccir Diophcintine equations: An algebraic approach
    • A. Tarlecki, editor, Springer-Verlag, September
    • E. Domenjoud. Solving systems of linccir Diophcintine equations: An algebraic approach. In A. Tarlecki, editor, Proceedings 16th MFCS, Kazimierz Dolny (Poland), LNCS 520, pages 141-150. Springer-Verlag, September 1991.
    • (1991) Proceedings 16th MFCS, Kazimierz Dolny (Poland), LNCS , vol.520 , pp. 141-150
    • Domenjoud, E.1
  • 10
    • 84886272087 scopus 로고    scopus 로고
    • Personal communication, June
    • A. Durctnd. Personal communication, June 1999.
    • (1999)
    • Durctnd, A.1
  • 11
    • 0022160742 scopus 로고
    • On the reduction method for integer linccir programs II
    • A. A. Elimcim and S. E. Elmaghraby. On the reduction method for integer linccir programs II. Discrete Applied Mathematics, 12(3):241-260, 1985.
    • (1985) Discrete Applied Mathematics , vol.12 , Issue.3 , pp. 241-260
    • Elimcim, A.A.1    Elmaghraby, S.E.2
  • 12
    • 85016879743 scopus 로고
    • Associative commutative unification
    • F. Fages. Associative commutative unification. Journal of Symbolic Computation, 3(3):257-275, 1987.
    • (1987) Journal of Symbolic Computation , vol.3 , Issue.3 , pp. 257-275
    • Fages, F.1
  • 14
    • 0002839351 scopus 로고
    • Ueber die Auflosung linearen Gleichungen mit reellen Coefficienten
    • P. Gordan. Ueber die Auflosung linearen Gleichungen mit reellen Coefficienten. Mathematische Annalen, 6:23-28, 1873.
    • (1873) Mathematische Annalen , vol.6 , pp. 23-28
    • Gordan, P.1
  • 15
    • 0000596483 scopus 로고
    • Ueber die Theorie der algebreuschen Formen
    • D. Hilbert. Ueber die Theorie der algebreuschen Formen. Mathematische Annalen, 36:473-534, 1890.
    • (1890) Mathematische Annalen , vol.36 , pp. 473-534
    • Hilbert, D.1
  • 16
    • 0013317944 scopus 로고
    • The complexity of counting problems in equational matching
    • M. Hermann Jind P. G. Kolaitis. The complexity of counting problems in equational matching. Journal of Symbolic Computation, 20(3):343-362, 1995.
    • (1995) Journal of Symbolic Computation , vol.20 , Issue.3 , pp. 343-362
    • Hermann Jind, M.1    Kolaitis, P.G.2
  • 17
    • 84947910987 scopus 로고
    • Computational complexity of simultaneous elementary matching problems
    • J. Wiedermann and P. Hdjek, editors. Springer-Verlag, August
    • M. Hermann and P. G. Kolaitis. Computational complexity of simultaneous elementary matching problems. In J. Wiedermann and P. Hdjek, editors. Proceedings 20th MFCS, Prague (Czech Republic), LNCS 969, pages 359-370. Springer-Verlag, August 1995.
    • (1995) Proceedings 20th MFCS, Prague (Czech Republic), LNCS , vol.969 , pp. 359-370
    • Hermann, M.1    Kolaitis, P.G.2
  • 19
    • 0348243801 scopus 로고
    • An algorithm to generate the basis of solutions to homogeneous linear Diophantine equations
    • G. Huet. An aJgorithm to generate the basis of solutions to homogeneous linear Diophantine equations. Information Processing Letters, 7(3):144-147, 1978.
    • (1978) Information Processing Letters , vol.7 , Issue.3 , pp. 144-147
    • Huet, G.1
  • 20
    • 0004459681 scopus 로고
    • The satanic notations: Counting classes beyond # P and other definitional adventures
    • March
    • L. A. Hemaspaandra and H. Vollmer. The satanic notations: Counting classes beyond # P and other definitional adventures. SIGACT News, 26(1):2-13, March 1995.
    • (1995) SIGACT News , vol.26 , Issue.1 , pp. 2-13
    • Hemaspaandra, L.A.1    Vollmer, H.2
  • 21
    • 0002692684 scopus 로고
    • Solving equations in abstract algebras: A rule-based survey of unification
    • J.-L. Lassez and G. Plotkin, editors, MIT Press, Cambridge (MA, USA)
    • J.-P. Jouannaud and C. Kirchner. Solving equations in abstract algebras: A rule-based survey of unification. In J.-L. Lassez and G. Plotkin, editors, Computational Logic. Essays in honor of Alan Robinson, chapter 8, pages 257-321. MIT Press, Cambridge (MA, USA), 1991.
    • (1991) Computational Logic. Essays in Honor of Alan Robinson, Chapter 8 , pp. 257-321
    • Jouannaud, J.-P.1    Kirchner, C.2
  • 23
    • 84886267808 scopus 로고    scopus 로고
    • Comptage de I'ensemble des elements de la base de Hilbert d'un systéme d'e ́quations diophsmtiennes lineaires
    • L. Juban. Comptage de I'ensemble des elements de la base de Hilbert d'un systéme d'e ́quations diophsmtiennes lineaires. Technical Report 98-R-066, LORIA, 1998.
    • (1998) Technical Report 98-R-066 LORIA
    • Juban, L.1
  • 24
    • 0001214779 scopus 로고
    • Une borne pour les générateurs des solutions entié res positives d'une é quation diophantienne lineaire
    • J.-L. Lambert. Une borne pour les générateurs des solutions entié res positives d'une é quation diophantienne lineaire. Compte-rendus de I'Acadimie des Sciences de Paris, 305(l):39-40, 1987.
    • (1987) Compte-rendus de i'Acadimie des Sciences de Paris , vol.305 , Issue.1 , pp. 39-40
    • Lambert, J.-L.1
  • 25
    • 0024622629 scopus 로고
    • Non-negative integer basis algorithms for linear equations with integer coefficients
    • D. Leinkford. Non-negative integer basis algorithms for linear equations with integer coefficients. Journal of Automated Reasoning, 5(l):25-35, 1989.
    • (1989) Journal of Automated Reasoning , vol.5 , Issue.1 , pp. 25-35
    • Leinkford, D.1
  • 26
    • 85006279726 scopus 로고
    • Adventures in associative-commutative unification
    • P. Lincoln and J. Christian. Adventures in associative-commutative unification. Journal of Symbolic Computation, 8(l-2):217-240, 1989.
    • (1989) Journal of Symbolic Computation , vol.8 , Issue.1-2 , pp. 217-240
    • Lincoln, P.1    Christian, J.2
  • 29
    • 84947931070 scopus 로고
    • Minimal solutions of lineau: Diophantine systems: Bounds and algorithms
    • R.V. Book, editor. Springer-Verlag, April
    • L. Pottier. Minimal solutions of lineau: Diophantine systems: bounds and algorithms. In R.V. Book, editor. Proceedings 4th RTA, Como (Italy), LNCS 488, pages 162-173. Springer-Verlag, April 1991.
    • (1991) Proceedings 4th RTA, Como (Italy), LNCS , vol.488 , pp. 162-173
    • Pottier, L.1
  • 31
    • 85168133352 scopus 로고
    • A complete unification stlgorithm for associative-commutative functions
    • M. Stickel. A complete unification stlgorithm for associative-commutative functions. In Proceedings 4th IJCAI, Tbilisi (USSR), pages 71-82, 1975.
    • (1975) Proceedings 4th IJCAI, Tbilisi (USSR) , pp. 71-82
    • Stickel, M.1
  • 32
    • 84976741234 scopus 로고
    • A unification algorithm for associative-commutative functions
    • M. Stickel. A unification algorithm for associative-commutative functions. Journal of the Association for Computing Machinery, 28(3):423-434, 1981.
    • (1981) Journal of the Association for Computing Machinery , vol.28 , Issue.3 , pp. 423-434
    • Stickel, M.1
  • 34
    • 0342313347 scopus 로고
    • PhD thesis, Tokyo Institute of Technology, Department of Computer Science, Tokyo, Japan
    • S. Toda. Computational complexity of counting complexity classes. PhD thesis, Tokyo Institute of Technology, Department of Computer Science, Tokyo, Japan, 1991.
    • (1991) Computational Complexity of Counting Complexity Classes
    • Toda, S.1
  • 35
    • 0026879923 scopus 로고
    • Polynomial-time 1-Turing reductions fi-om #PH to # P
    • S. Toda and O. Watanabe. Polynomial-time 1-Turing reductions fi-om #PH to # P. Theoretical Computer Science, 100(1):205-221, 1992.
    • (1992) Theoretical Computer Science , vol.100 , Issue.1 , pp. 205-221
    • Toda, S.1    Watanabe, O.2
  • 36
    • 49249151236 scopus 로고
    • The complexity of computing the permcinent
    • L. G. Valiant. The complexity of computing the permcinent. Theoretical Computer Science, 8(2):189-201, 1979.
    • (1979) Theoretical Computer Science , vol.8 , Issue.2 , pp. 189-201
    • Valiant, L.G.1
  • 37
    • 0000142982 scopus 로고
    • The complexity of enumeration and eUability problems
    • L. G. Valiant. The complexity of enumeration and eUability problems. SIAM Journal on Computing, 8(3):410-421, 1979.
    • (1979) SIAM Journal on Computing , vol.8 , Issue.3 , pp. 410-421
    • Valiant, L.G.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.