Combinatorial characterizations of extractors and Kolmogorov extractors

نویسنده

  • Marius Zimand
چکیده

We present characterizations of extractors and Kolmogorov extractors in terms of a combinatorial object called balanced table. These characterizations provide an alternative proof for the relation between extractors and Kolmogorov extractors, first obtained in [FHP06] and [HPV09].

برای دانلود 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

Nearly Optimal Language Compression Using Extractors

We show two sets of results applying the theory of extractors to resource-bounded Kolmogorov complexity: Most strings in easy sets have nearly optimal polynomial-time CD complexity. This extends work of Sipser Sip83] and Buhrman and Fortnow BF97]. We use extractors to extract the randomness of strings. In particular we show how to get from an arbitrary string, an incompressible string which enc...

متن کامل

Possibilities and impossibilities in Kolmogorov complexity extraction

Randomness extraction is the process of constructing a source of randomness of high quality from one or several sources of randomness of lower quality. The problem can be modeled using probability distributions and min-entropy to measure their quality and also by using individual strings and Kolmogorov complexity to measure their quality. Complexity theorists are more familiar with the first ap...

متن کامل

Space-Bounded Kolmogorov Extractors

An extractor is a function that receives some randomness and either “improves” it or produces “new” randomness. There are statistical and algorithmical specifications of this notion. We study an algorithmical one called Kolmogorov extractors and modify it to resourcebounded version of Kolmogorov complexity. Following Zimand we prove the existence of such objects with certain parameters. The uti...

متن کامل

Extractors and an efficient variant of Muchnik's theorem

Muchnik's theorem about simple conditional descriprion states that for all words $a$ and $b$ there exists a short program $p$ transforming $a$ to $b$ that has the least possible length and is simple conditional on $b$. This paper presents a new proof of this theorem, based on extractors. Employing the extractor technique, two new versions of Muchnik's theorem for space- and time-bounded Kolmogo...

متن کامل

Extracting Randomness: How and Why - A survey - Computational Complexity, 1996. Proceedings., Eleventh Annual IEEE Conference on

Extractors are boolean functions that allow, in some precise sense, extraction o f randomness from somewhat random distributions. Extractors, and the closely related “Dispersers”, exhibit some of the most “random-like” properties of explicitly constructed combinatorial structures. In turn, extractors and dispersers have many applications in “removing randomness” in various settings, and in maki...

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

برای دانلود 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

عنوان ژورنال:

دوره   شماره 

صفحات  -

تاریخ انتشار 2010