An optimal lower bound for turing machines with one work tape and a two-way input tape

  • Wolfgang Maass
  • Georg Schnitger
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 223)


This paper contains the first concrete lower bound argument for Turing machines with one work tape and a two-way input tape (these Turing machines are often called "offline 1-tape Turing machines"). In particular we prove an optimal lower bound of Ω(n3/2/(log n)1/2) for transposing a matrix with elements of bit length ∘(logn) (where n is the length of the total input). This implies a lower bound of Ω(n3/2/(log n)1/2) for sorting on the considered type of Turing machine. We also get as corollaries the first nonlinear lower bound for the most difficult version of the two tapes — versus — one problem, and a separation of the considered type of Turing machine from that with an additional write-only output tape.


Turing Machine Kolmogorov Complexity Input Tape Matrix Transposition Output Tape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 1986

Authors and Affiliations

  • Wolfgang Maass
    • 1
  • Georg Schnitger
    • 2
  1. 1.Department of MathematicsStatistics and Computer Science University of Illinois at ChicagoChicago
  2. 2.Department of Computer SciencePennsylvania State UniversityUniversity Park

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