Separating ⊕L from L, NL, co-NL and AL (=P) for Oblivious turing machines of linear access time

  • Matthias Krause
Part of the Lecture Notes in Computer Science book series (LNCS, volume 452)


We present a new lower bound argument for oblivious parity-branching programs which allows to prove exponential lower bounds on the width if the length is restricted to be linear or at most o(n · log(n)). This solves an open problem because "Cut & Paste" arguments which provided bounds of the same quality in the case of determinism, nondeterminism, and co-nondeterminism [AM86] [KMW89] do not work in the case of parity-acceptation. Our technique is applicable to some well-known decision problems such as the graph-accessibility-problem of directed graphs, and the word problems of free groups of finite rank. Using well-known results on the simulation of logspace-bounded Turing machines by sequences of branching programs we give at least the complete separation of the complexity classes L, NL, co-NL, ⊕L, and AL=P for oblivious Turing machines of linear access time.


Directed Graph Word Problem Turing Machine Complexity Class Query Node 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1990

Authors and Affiliations

  • Matthias Krause
    • 1
  1. 1.Humboldt-Universitaet zu Berlin, Sektion MathematikBerlinG.D.R.

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