The complexity of matrix transposition on one-tape off-line Turing machines

Martin Dietzfelbinger, Wolfgang Maass, Georg Schnitger
1991 Theoretical Computer Science  
Dietzfelbinger, M., W. Maass and G. Schnitger, The complexity of matrix transposition on one-tape off-line Turing machines, Theoretical Computer Science, 82 (1991) 113-129. This paper contains the first concrete lower bound argument for Turing machines with one worktape and a two-way input tape ("one-tape o&line Turing machines"): an optimal lower bound of a( n * I/ [(log(l)/p)"21) for transposing an 1 x l-matrix with elements of bit length p on such machines is proved. (The length of the input
more » ... is denoted by n.) A special case is a lower bound of fl(n312/(!og n)"') for transposing Boolean 1 xl-matrices (n = 12) on such Turing machines. The proof of the matching upper bound (which is nontrivial for p < log 1) uses the fact that one-tape off-line Turing machines can copy strings slightly faster than if the straightforward method is used. As a corollary of the lower bound it is shown that sorting n/(3 log n) strings of 3 log n bits each takes R(n312/(log n)"') steps on one-tape off-line Turing machines. Further corollaries give the first non-linear lower bound for the version of the two-tapes-versus-one problem concerning one-tape off-line Turing machines, and separate one-tape off-line Turing machines from those Turing machines with one input tape, one worktape, and an additional write-only output tape.
doi:10.1016/0304-3975(91)90175-2 fatcat:fkt4rvugerhqzinuaqpukhzqde