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

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

Abstract

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.

Keywords

Directed Graph Word Problem Turing Machine Complexity Class Query Node 
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.

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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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