Projection Complete Graph Problems Corresponding to a Branching-Program-Based Characterization of the Complexity Classes NC1 ,Land NL

  • Christoph Meinel


The p-projection completeness of some restricted graph accessibility problems for the (nonuniform) complexity classes NC 1 L and NL will be proved by means of branching-program-based characterizations of these classes. A simulation result concerning polynomial-size, bounded-width disjunctive branching programs and polynomial-size, bounded-width usual ones yields that NC 1=L implies L=NL. Some consequences of these results for separating these classes are discussed.


Boolean Function Turing Machine Complexity Class Boolean Variable Bounded Width 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. /Ba86/.
    D.A.Barrington, ‘Bounded width polynomial-size branching programs recognizing exactly those languages in NC1, Proc. 18-th STOC, 1986, 1–5Google Scholar
  2. /CSV84/.
    A.K.Chandra, L.Stockmeyer, U.Vishkin, ‘Constant depth reducibility’, SIAM J.Comput. 13, No. 2,1984, 423–439MathSciNetMATHCrossRefGoogle Scholar
  3. /FSS81/.
    M.Furst, J.B.Saxe, M.Sipser, ‘Parity, circuits and the polynomial-time hierarchy’, Proc. 22-th FOCS, 1981, 260–270Google Scholar
  4. /KL80/.
    R.M.Karp, R.J.Lipton, ‘Some connections between nonuniform and uniform complexity classes’, Proc. 12-th STOC, 1980, 302–309Google Scholar
  5. /Me86/.
    Ch.Meinel, ‘L (nonuniform) and NL (nonuniform)’, Proc. MFCS-86 (Bratislava), 1986Google Scholar
  6. /Sa70/.
    W.Savitch, ‘Relations between nondeterministic and deterministic tape complexities’, J. Comp. and Sys.Sc. 4, 1970, 177–192MathSciNetMATHCrossRefGoogle Scholar
  7. /SV81/.
    S.Skyum, L.G.Valiant, ‘A complexity theory based on Boolean algebra’, Proc. 22-th FOCS, 1981, 244–253Google Scholar

Copyright information

© Plenum Press, New York 1987

Authors and Affiliations

  • Christoph Meinel
    • 1
  1. 1.Sektion MathematikHumboldt-UniversitätBerlinGermany

Personalised recommendations