On Ajtai's Lower Bound Technique for -way Branching Programs and
the Hamming Distance Problem
Jakob Pagter May 2000 |

## Abstract:
In this report we study the proof employed by Miklos Ajtai
[
Determinism versus Non-Determinism for Linear Time RAMs with Memory
Restrictions, 31st Symposium on Theory of Computation (STOC), 1999] when
proving a non-trivial lower bound in a general model of computation for the
Hamming distance problem: given elements decide whether any two of them
have ``small'' Hamming distance. Specifically, Ajtai was able to show that
any -way branching program deciding this problem using time must
use space
. We generalize Ajtai's original proof allowing us
to prove a time-space trade-off for deciding the Hamming distance problem in
the -way branching program model for time between and ,
for some suitable . In particular we prove that if space is
, then time is
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