The Roman Catholic Church Today : A Protestant View

London88hlm.; 19x12,5 c

The Roman Catholic Church Today : A Protestant View

London88 p.; 19 c

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

AbstractThis paper contains the first concrete lower bound argument for Turing machines with one worktape and a two-way input tape (“one-tape off-line Turing machines”): an optimal lower bound of Ω(n·l/⌈(log(l)p)12⌉) for transposing an I × l-matrix with elements of bit length p on such machines is proved. (The length of the input is denoted by n.) A special case is a lower bound of Ω(n32(log n)12) for transposing Boolean l × l-matrices (n = l2) on such Turing machines. The proof of the matching upper bound (which is nontrivial for p<logl) 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 Ω(n32(log n)12)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

26. Workshop uber Komplexitätstheorie, Datenstrukturen und effiziente Algorithmen, TU-Berlin

L&lt;Fnan&gt; 6= 1UL 18.05 Ende Universal hashing and k-wise independent random variables via integer arithmetic without primes Martin Dietzfelbinger Fachbereich Informatik, Universitat Dortmund, Germany email: [email protected] Let u; m 1 be arbitrary integers and let r um be any multiple of m. The main result of this talk is that the multiset H = fh a;b j 0 a; b ! rg of functions from U = f0; : : : ; u \Gamma 1g to M = f0; : : : ; m \Gamma 1g, where h a;b (x) = ((ax + b) mod r) div (r=m);&lt;