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Electronic Colloquium on Computational Complexity

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Reports tagged with martingale:
TR98-058 | 2nd August 1998
H. Buhrman, Dieter van Melkebeek, K.W. Regan, Martin Strauss, D. Sivakumar

A Generalization of Resource-Bounded Measure, With Application to the BPP vs. EXP Problem

We introduce "resource-bounded betting games", and propose
a generalization of Lutz's resource-bounded measure in which the choice
of next string to bet on is fully adaptive. Lutz's martingales are
equivalent to betting games constrained to bet on strings in lexicographic
order. We show that if strong pseudo-random number generators exist,
more >>>

TR11-074 | 27th April 2011
Ludwig Staiger

Exact constructive dimension

Revisions: 1

The present paper generalises results by Lutz and Ryabko. We prove a
martingale characterisation of exact Hausdorff dimension. On this base we
introduce the notion of exact constructive dimension of (sets of) infinite

Furthermore, we generalise Ryabko's result on the Hausdorff dimension of the
... more >>>

TR17-168 | 5th November 2017
Amos Beimel, Iftach Haitner, Nikolaos Makriyannis, Eran Omri

Tighter Bounds on Multi-Party Coin Flipping, via Augmented Weak Martingales and Di erentially Private Sampling

Revisions: 6

In his seminal work, Cleve [STOC 1986] has proved that any r-round coin-flipping protocol can be efficiently biassed by ?(1/r). The above lower bound was met for the two-party case by Moran, Naor, and Segev [Journal of Cryptology '16], and the three-party case (up to a polylog factor) by Haitner ... more >>>

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