메뉴 건너뛰기




Volumn 23, Issue 3, 2007, Pages 359-379

On the complexity of deciding connectedness and computing Betti numbers of a complex algebraic variety

Author keywords

Betti numbers; Connected components; Lower bounds; PSPACE

Indexed keywords

ALGEBRA; COMPUTATIONAL COMPLEXITY; INTEGER PROGRAMMING; POLYNOMIALS; PROBLEM SOLVING;

EID: 34249680239     PISSN: 0885064X     EISSN: 10902708     Source Type: Journal    
DOI: 10.1016/j.jco.2007.03.008     Document Type: Article
Times cited : (26)

References (15)
  • 1
    • 33749163668 scopus 로고    scopus 로고
    • Computing the first few Betti numbers of semi-algebraic sets in single exponential time
    • Basu S. Computing the first few Betti numbers of semi-algebraic sets in single exponential time. J. Symbolic Comput. 41 10 (2006) 1125-1154
    • (2006) J. Symbolic Comput. , vol.41 , Issue.10 , pp. 1125-1154
    • Basu, S.1
  • 2
    • 34249725244 scopus 로고    scopus 로고
    • J. Bochnak, M. Coste, M.F. Roy, Real Algebraic Geometry, Ergebnisse der Mathematik und ihrer Grenzgebiete, 3. Folge, vol. 36, Springer, 1998.
  • 3
    • 34249712613 scopus 로고    scopus 로고
    • G.E. Bredon, Topology and geometry, Graduate Texts in Mathematics, vol. 139, Springer, New York, 1997.
  • 4
    • 12144287888 scopus 로고    scopus 로고
    • Counting complexity classes for numeric computations I: semilinear sets
    • Bürgisser P., and Cucker F. Counting complexity classes for numeric computations I: semilinear sets. SIAM J. Comput. 33 (2003) 227-260
    • (2003) SIAM J. Comput. , vol.33 , pp. 227-260
    • Bürgisser, P.1    Cucker, F.2
  • 5
    • 34249699233 scopus 로고    scopus 로고
    • P. Bürgisser, F. Cucker, Variations by complexity theorists on three themes of Euler, Bézout, Betti, and Poincaré, in: J. Krajicek (Ed.), Complexity of Computations and Proofs, Quaderni di Matematica, vol. 13, Department of Mathematics, Seconda Università di Napoli, Caserta, Napoli, Italy, 2005, pp. 73-152.
  • 6
    • 31644440700 scopus 로고    scopus 로고
    • Counting complexity classes for numeric computations II: algebraic and semialgebraic sets
    • Bürgisser P., and Cucker F. Counting complexity classes for numeric computations II: algebraic and semialgebraic sets. J. Complexity 22 (2006) 147-191
    • (2006) J. Complexity , vol.22 , pp. 147-191
    • Bürgisser, P.1    Cucker, F.2
  • 7
    • 33751051746 scopus 로고    scopus 로고
    • The complexity of semilinear problems in succinct representation
    • Bürgisser P., Cucker F., and de Naurois P. The complexity of semilinear problems in succinct representation. Comput. Complexity 15 3 (2006) 197-235
    • (2006) Comput. Complexity , vol.15 , Issue.3 , pp. 197-235
    • Bürgisser, P.1    Cucker, F.2    de Naurois, P.3
  • 8
    • 84888229792 scopus 로고    scopus 로고
    • J. Canny, Some algebraic and geometric computations in PSPACE, in: Proceedings of the 20th Annual ACM STOC, 1988, pp. 460-467.
  • 9
    • 34249739320 scopus 로고    scopus 로고
    • E.M. Friedlander, B. Mazur, Filtrations on the homology of algebraic varieties, Mem. Amer. Math. Soc. 110 (529) (1994) ix+110.
  • 10
    • 34249695087 scopus 로고    scopus 로고
    • J. Harris, Algebraic geometry, Graduate Texts in Mathematics, vol. 133, Springer, New York, 1992.
  • 11
    • 0004193355 scopus 로고    scopus 로고
    • Cambridge University Press, Cambridge
    • Hatcher A. Algebraic Topology (2002), Cambridge University Press, Cambridge
    • (2002) Algebraic Topology
    • Hatcher, A.1
  • 12
    • 0024910920 scopus 로고
    • Polynomial space counting problems
    • Ladner R.E. Polynomial space counting problems. SIAM J. Comput. 18 6 (1989) 1087-1097
    • (1989) SIAM J. Comput. , vol.18 , Issue.6 , pp. 1087-1097
    • Ladner, R.E.1
  • 13
    • 0018730847 scopus 로고    scopus 로고
    • J.H. Reif, Complexity of the mover's problem and generalizations, in: Proceedings of 20th FOCS, 1979, pp. 421-427.
  • 14
    • 0002455895 scopus 로고
    • Complexity of the generalized mover's problem
    • Schwartz J.T., Sharir M., and Hopcroft J. (Eds), Ablex Publishing Corporation
    • Reif J.H. Complexity of the generalized mover's problem. In: Schwartz J.T., Sharir M., and Hopcroft J. (Eds). Planning, Geometry and Complexity of Robot Motion (1987), Ablex Publishing Corporation 267-281
    • (1987) Planning, Geometry and Complexity of Robot Motion , pp. 267-281
    • Reif, J.H.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.