Problems complete for ⊕L

  • Carsten Damm
Part III Communications
Part of the Lecture Notes in Computer Science book series (LNCS, volume 464)


L is the class of languages acceptable by logarithmic space bounded Turing machines that work nondeterministically and are equipped with parity-acceptance, i.e. an input word is accepted if and only if the number of possible correct computation paths on this input is odd. Several natural problems are shown to be complete for ⊕L under NC1-reductions. A consequence is that ⊕L is the F2-analogon of Cook's class DET, the class of problems NC1-reducible to the computation of determinants over Z.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [Be84]
    S.J. Berkowitz: On computing the determinant in small parallel time using a small number of processors, Information Processing Letters 18(1984), 147–150CrossRefGoogle Scholar
  2. [BvzGH82]
    A. Borodin,J.v.z. Gathen,J. Hopcroft: Fast parallel matrix and GCD computations, Information and Control 52(1982),241–256CrossRefGoogle Scholar
  3. [Co85]
    S.A. Cook: A taxonomy of problems with fast parallel algorithms, Information and Control 64(1985), 2–22CrossRefGoogle Scholar
  4. [DM89]
    C.Damm,Ch.Meinel: Separating completely complexity classes related to polynomial size {⊕}-decision trees, Proc. FCT'89, LNCS 380, 127–136Google Scholar
  5. [IL89]
    N.Immermann,D.Landau: The complexity of iterated multiplication, Proc. 4th Structure in Complexity Theory Conference (1989),104–111Google Scholar
  6. [KMW88]
    M.Krause,Ch.Meinel,S.Waack: Separating the eraser Turing machine classes ℒe,Ne, co-Ne and P e, Proc. MFCS'88, LNCS 324, 405–413Google Scholar
  7. [KMW89]
    M.Krause,Ch.Meinel,S.Waack: Separating complexity classes related to certain input oblivious logarithmic space bounded Turing machines, Proc. 4th IEEE Structure in Complexity Theory Symposium, 1989Google Scholar
  8. [Kr89]
    M.Krause: Separating ⊕L from L, NL, co-NL and AL = P for oblivious Turing machines of linear acces time, to appear in Proc. MFCS'90, Springer Verlag, LNCS??Google Scholar
  9. [Me87]
    Ch.Meinel: Polynomial size Ω-branching programs and their computational power, to appear in Information and ComputationGoogle Scholar
  10. [Mu86]
    K.Mulmuley: A fast parallel algorithm to compute the rank of a matrix over an arbitrary field, Proc. 18th ACM STOC(1986), 338–339Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Carsten Damm
    • 1
  1. 1.Sektion MathematikHumboldt-Universität zu BerlinBerlin

Personalised recommendations