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- Krishna B. Athreya, John M. Hitchcock, Jack H. Lutz, Elvira Mayordomo
- SIAM J. Comput.
- 2004

The two most important notions of fractal dimension are Hausdorff dimension, developed by Hausdorff (1919), and packing dimension, developed independently by Tricot (1982) and Sullivan (1984). Both dimensions have the mathematical advantage of being defined from measures, and both have yielded extensive applications in fractal geometry and dynamical… (More)

- Elvira Mayordomo
- Electronic Colloquium on Computational Complexity
- 2001

Lutz [7] has recently developed a constructive version of Hausdorff dimension, using it to assign to every sequence A ∈ C a constructive dimension dim(A) ∈ [0,1]. Classical Hausdorff dimension [3] is an augmentation of Lebesgue measure, and in the same way constructive dimension augments Martin– Löf randomness. All Martin–Löf random sequences have… (More)

Supported by the Human Capital and Mobility Program of the European Community under grant CHRX-CT93-0415 (COLORET). Mathematisches Institut, Universit at Heidelberg, D-69120 Heidelberg, Germany Universidad de Zaragoza, Dept. Inform atica, CPS, Mar a del Luna 3, E-50015 Zaragoza, Spain We survey recent results on resource-bounded measure and randomness in… (More)

- Elvira Mayordomo
- Theor. Comput. Sci.
- 1992

A set A is P-bi-immune if neither A nor its complement has an innnite subset in P. We investigate here the abundance of P-bi-immune languages in linear-exponential time (E). We prove that the class of P-bi-immune sets has measure 1 in E. This implies thatàlmost' every language in E is P-bi-immune, that is to say, almost every set recognizable in linear… (More)

- Jack Jie Dai, James I. Lathrop, Jack H. Lutz, Elvira Mayordomo
- ICALP
- 2001

- Jack H. Lutz, Elvira Mayordomo
- SIAM J. Comput.
- 1993

Ogiwara and Watanabe have recently shown that the hypothesis P not equal NP implies that no (polynomially) sparse language is polynomial-time btt-hard for NP. Their technique does not appear to allow significant relaxation of either the query bound or the sparseness criterion. It is shown here that a stronger hypothesis --namely, that NP does not have… (More)

- Klaus Ambos-Spies, Elvira Mayordomo, Yongge Wang, Xizhong Zheng
- STACS
- 1996

We introduce balanced t(n)-genericity which is a reenement of the genericity concept of Ambos-Spies, Fleischhack and Huwig 2] and which in addition controls the frequency with which a condition is met. We show that this concept coincides with the resource-bounded version of Church's stochasticity 6]. By uniformly describing these concepts and weaker notions… (More)

- Jack H. Lutz, Elvira Mayordomo
- Bulletin of the EATCS
- 1999

- Jack H. Lutz, Elvira Mayordomo, TR
- 1992

Under the hypothesis that NP does not have p-measure 0 (roughly, that NP contains more than a negligible subset of exponential time), it is show n that there is a language that is polynomial-time Turing complete (``Cook complete''), but not polynomial-time many-one complete (``Karp-Levin complete''), for NP. This conclusion, widely believed to be true, is… (More)

- John M. Hitchcock, Jack H. Lutz, Elvira Mayordomo
- ICALP
- 2003

Resource-bounded dimension is a complexity-theoretic extension of classical Hausdorff dimension introduced by Lutz (2000) in order to investigate the fractal structure of sets that have resource-bounded measure 0. For example, while it has long been known that the Boolean circuit-size complexity class SIZE ( α n