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Electronic Colloquium on Computational Complexity

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All reports by Author Elvira Mayordomo:

TR09-022 | 16th February 2009
Jack H. Lutz, Elvira Mayordomo

Inseparability and Strong Hypotheses for Disjoint NP Pairs

Revisions: 1

This paper investigates the existence of inseparable disjoint
pairs of NP languages and related strong hypotheses in
computational complexity. Our main theorem says that, if NP does
not have measure 0 in EXP, then there exist disjoint pairs of NP
languages that are P-inseparable, in fact TIME(2^(n^k)-inseparable.
We also relate ... more >>>

TR08-037 | 29th February 2008
Xiaoyang Gu, Jack H. Lutz, Elvira Mayordomo

Curves That Must Be Retraced

Revisions: 1

We exhibit a polynomial time computable plane curve GAMMA that has finite length, does not intersect itself, and is smooth except at one endpoint, but has the following property. For every computable parametrization f of GAMMA and every positive integer n, there is some positive-length subcurve of GAMMA that f ... more >>>

TR07-051 | 18th April 2007
Pilar Albert, Elvira Mayordomo, Philippe Moser

Bounded Pushdown dimension vs Lempel Ziv information density

In this paper we introduce a variant of pushdown dimension called bounded pushdown (BPD) dimension, that measures the density of information contained in a sequence, relative to a BPD automata, i.e. a finite state machine equipped with an extra infinite memory stack, with the additional requirement that every input symbol ... 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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TR04-029 | 7th April 2004
John Hitchcock, Maria Lopez-Valdes, Elvira Mayordomo

Scaled dimension and the Kolmogorov complexity of Turing hard sets

Scaled dimension has been introduced by Hitchcock et al (2003) in order to quantitatively distinguish among classes such as SIZE(2^{a n}) and SIZE(2^{n^{a}}) that have trivial dimension and measure in ESPACE.

more >>>

TR01-059 | 20th July 2001
Elvira Mayordomo

A Kolmogorov complexity characterization of constructive Hausdorff dimension

Revisions: 3

We obtain the following full characterization of constructive dimension
in terms of algorithmic information content. For every sequence A,
cdim(A)=liminf_n (K(A[0..n-1])/n.

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