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Electronic Colloquium on Computational Complexity

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TR05-159 | 14th November 2005
Daniel Rolf

Improved Bound for the PPSZ/Schöning-Algorithm for $3$-SAT

The PPSZ Algorithm presented by Paturi, Pudlak, Saks, and Zane in 1998 has the nice feature that the only satisfying solution of a uniquely satisfiable $3$-SAT formula can be found in expected running time at most $O(1.3071^n)$. Its bound degenerates when the number of solutions increases. In 1999, Schöning proved ... more >>>


TR05-158 | 12th December 2005
Chris Peikert, Alon Rosen

Efficient Collision-Resistant Hashing from Worst-Case Assumptions on Cyclic Lattices

The generalized knapsack function is defined as $f_{\a}(\x) = \sum_i
a_i \cdot x_i$, where $\a = (a_1, \ldots, a_m)$ consists of $m$
elements from some ring $R$, and $\x = (x_1, \ldots, x_m)$ consists
of $m$ coefficients from a specified subset $S \subseteq R$.
Micciancio ... more >>>


TR05-157 | 10th December 2005
Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo

Points on Computable Curves

The ``analyst's traveling salesman theorem'' of geometric
measure theory characterizes those subsets of Euclidean
space that are contained in curves of finite length.
This result, proven for the plane by Jones (1990) and
extended to higher-dimensional Euclidean spaces by
Okikiolu (1991), says that a bounded set $K$ is contained
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