Scaled Dimension of Individual Strings

نویسنده

  • María López-Valdés
چکیده

We define a new discrete version of scaled dimension and we find connections between the scaled dimension of a string and its Kolmogorov complexity and predictability. We give a new characterization of constructive scaled dimension by Kolmogorov complexity, and prove a new result about scaled dimension and prediction.

برای دانلود رایگان متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید

ثبت نام

اگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید

منابع مشابه

A Characterization of Constructive Dimension

In the context of Kolmogorov’s algorithmic approach to the foundations of probability, Martin-Löf defined the concept of an individual random sequence using the concept of a constructive measure 1 set. Alternate characterizations use constructive martingales and measures of impossibility. We prove a direct conversion of a constructive martingale into a measure of impossibility and vice versa, s...

متن کامل

The Dimensions of Individual Strings and Sequences

A constructive version of Hausdorff dimension is developed using constructive supergales, which are betting strategies that generalize the constructive supermartingales used in the theory of individual random sequences. This constructive dimension is used to assign every individual (infinite, binary) sequence S a dimension, which is a real number dim(S) in the interval [0, 1]. Sequences that ar...

متن کامل

The (non-)existence of perfect codes in Lucas cubes

A Fibonacci string of length $n$ is a binary string $b = b_1b_2ldots b_n$ in which for every $1 leq i < n$, $b_icdot b_{i+1} = 0$. In other words, a Fibonacci string is a binary string without 11 as a substring. Similarly, a Lucas string is a Fibonacci string $b_1b_2ldots b_n$ that $b_1cdot b_n = 0$. For a natural number $ngeq1$, a Fibonacci cube of dimension $n$ is denoted by $Gamma_n$ and i...

متن کامل

Investigating the Relationship between National Dimension of Individual Identity and Individual Differentiation by Communicating Communicative Mediation and Social Identity Cycle

Individual identity is self-explanatory by emphasizing its difference from others. In this study, we examine the impact of nationalism on the degree of individual differentiation by communicating comm::::union:::: and social identity. The research method of correlation method is structural equation modeling. The statistical population includes all citizens over 15 years of age in the provinces ...

متن کامل

Nanometric-Scaled Emulsions (Nanoemulsions)

Nanotechnology, shortened to nanotech, is the study of the controlling of matter on an atomic and molecular scale. Generally, nanotechnology deals with structures sized between 1 to 100 nanometer in at least one dimension and involves developing materials or devices within that size. The use of nanotechnology in the field of pharmaceutics and drug delivery has grown over the last few years, so ...

متن کامل

ذخیره در منابع من


  با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید

عنوان ژورنال:
  • Electronic Colloquium on Computational Complexity (ECCC)

دوره 13  شماره 

صفحات  -

تاریخ انتشار 2006