Effective dimension
نویسندگان
چکیده
منابع مشابه
Effective Algebra and Effective Dimension
Effective Dimension is a notion introduced by Lutz, which measures the density of information in an infinite sequence. Lutz asks how this concept interacts with classical topological notions. In Chapter two, I present several results concerning this. Effective Algebra is the study of computable and relatively computable structures and the relations on them. In Chapter three, I present several r...
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We continue the study of effective Hausdorff dimension as it was initiated by LUTZ. Whereas he uses a generalization of martingales on the Cantor space to introduce this notion we give a characterization in terms of effective s-dimensional Hausdorff measures, similar to the effectivization of Lebesgue measure by MARTIN-LÖF. It turns out that effective Hausdorff dimension allows to classify sequ...
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Lutz (2000) has recently proved a new characterization of Hausdorff dimension in terms of gales, which are betting strategies that generalize martingales. We present here this characterization and give three instances of how it can be used to define effective versions of Hausdorff dimension in the contexts of constructible, finite-state, and resource-bounded computation.
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Practitioners have long noticed that quasi-Monte Carlo methods work very well on functions that are nearly superpositions of low dimensional functions. The reason is that the low dimensional coordinate projections of QMC rules can have very good equidistribution properties at sample sizes for which the original rule itself cannot have good equidistribution. This paper explores a converse propos...
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In this paper we discuss various aspects of the problem of determining the minimal dimension of an injective linear representation of a finite semigroup over a field. We outline some general techniques and results, and apply them to numerous ex-
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ژورنال
عنوان ژورنال: Journal of Algebra
سال: 1976
ISSN: 0021-8693
DOI: 10.1016/0021-8693(76)90189-7