The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
Filters
Kolmogorov Complexity Theory over the Reals
[article]
2008
arXiv
pre-print
Preserved Fulltext
Other Versions
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory -- in the discrete setting of bits and Turing machines. ...
Over real numbers, on the other hand, the BSS-machine (aka real-RAM) has been established as a major model of computation. ...
Finally we owe to Klaus Meer for pointing us to the seminal work of Montaña and Pardo who first introduced real Kolmogorov Complexity. ...
arXiv:0802.2027v2
fatcat:y2wdj23bjjd27fszs5xto5legq
Kolmogorov Complexity Theory over the Reals
2008
Electronical Notes in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Kolmogorov Complexity constitutes an integral part of computability theory, information theory, and computational complexity theory-in the discrete setting of bits and Turing machines. ...
Over real numbers, on the other hand, the BSS-machine (aka real-RAM) has been established as a major model of computation. ...
Finally we owe to Klaus Meer for pointing us to the seminal work of Montaña and Pardo who first introduced real Kolmogorov Complexity. ...
doi:10.1016/j.entcs.2008.12.014
fatcat:iulx5fjenzbwxmig2y63r3icnu
On the Kolmogorov complexity of continuous real functions
2013
Annals of Pure and Applied Logic
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
An asymptotic bound on the Kolmogorov complexities of total single-valued computable real functions will be presented as well. ...
Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects-such as rational numbers-used to ...
Montaña and Pardo [17] and Ziegler and Koolen [25] have studied Kolmogorov complexity over sequences of real numbers based on the theory of real Turing machines. ...
doi:10.1016/j.apal.2012.11.003
fatcat:xjky2cr3vrcldlgikehn7uqxz4
Page 10262 of Mathematical Reviews Vol. , Issue 2004m
[page]
2004
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
The paper addresses a question on the Kolmogorov complexity of
reals. ...
Using prefix-free Kolmogorov complexity <j as a reducibil- ity on the set of all reals, it proves that there are continuum many H-degrees in the random reals. ...
Complexities Approach to Two Problems In Number Theory
[article]
2016
arXiv
pre-print
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
Other Versions
problems in the non-logical discipline.Futhermore,we show that resource-bounded Kolmogorov Complexity and computational complexity can at least provide tips or principles to mathematical problems in the ...
By Kolmogorov Complexity,two number-theoretic problems are solved in different way than before,one problem is Maxim Kontsevich and Don Bernard Zagier's Problem 3 Exhibit at least one number which does ...
question by Kolmogorov Complexity. ...
arXiv:1610.04026v3
fatcat:5udl5eurnzh63c6ysh6b7kta6y
Is Randomness Native to Computer Science? Ten Years After
[chapter]
2011
Randomness Through Computation
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
I remember that Kolmogorov built the mathematical theory of the so-called Kolmogorov complexity out of this paradox. ...
Shannon proved that the functions over the reals which are computed by GPACs are exactly the solutions of algebraic differential systems. ...
doi:10.1142/9789814327756_0019
fatcat:lxjyg53fzzb2nlqb6i4oofiicy
On the Kolmogorov Complexity of Continuous Real Functions
[chapter]
2011
Lecture Notes in Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
An asymptotic bound on the Kolmogorov complexities of total single-valued computable real functions will be presented as well. ...
Later, the definition was extended to real numbers based on the asymptotic behaviour of the sequence of the Kolmogorov complexities of the finitely-representable objects-such as rational numbers-used to ...
I would also like to thank Douglas Cenzer and Willem Fouché for informing me of their related work on the subject of algorithmic randomness over function spaces. ...
doi:10.1007/978-3-642-21875-0_9
fatcat:6pbcuw4ydvbqtox7hkkczztu3q
Page 5977 of Mathematical Reviews Vol. , Issue 94j
[page]
1994
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Chapter 2 (“Algorithmic complexity”) is dedicated to the theory of the most general form of Kolmogorov complexity, called in the book the plain Kolmogorov complex- ity. ...
Kolmogorov complexity is the theory which explains such dis- crepancies and explores the properties and capabilities of objects like the ones above. ...
Page 4394 of Mathematical Reviews Vol. , Issue 2002F
[page]
2002
Mathematical Reviews
Preserved Fulltext
The Internet Archive has digitized a microfilm copy of this work. It may be possible to borrow a copy for reading.
Summary: “We consider for a real number a the Kolmogorov complexities of its expansions with respect to different bases. ...
Philip Ross Watson (Bradford)
2002f:68067 68Q30
Staiger, Ludwig (D-MLU-II; Halle an der Saale)
The Kolmogorov complexity of real numbers. ...
Computability, Complexity and Randomness (Dagstuhl Seminar 12021)
2012
Dagstuhl Reports
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2022; you can also visit the original URL.
The file type is application/pdf.
Research on the notions of information and randomness has drawn on methods and ideas from computability theory and cumputational complexity, as well as core mathematical subjects like measure theory and ...
information theory. ...
Understanding the complexity of the reachability problem is a central concern of computational complexity theory. ...
doi:10.4230/dagrep.2.1.19
dblp:journals/dagstuhl-reports/BecherBDM12
fatcat:bkapirz4vfgkzcexiutm33k74q
Is Randomness "Native" to Computer Science?
[article]
2008
arXiv
pre-print
Preserved Fulltext
The Internet Archive has a preservation copy of this work in our general collections.
The file type is application/pdf.
We survey the Kolmogorov's approach to the notion of randomness through the Kolmogorov complexity theory. ...
The original motivation of Kolmogorov was to give up a quantitative definition of information. In this theory, an object is randomness in the sense that it has a large information content. ...
Such Borel sets are, in fact, coded in any inner submodel of set theory. -Solovay random reals over a submodel of set theory are reals outside every measure zero Borel set coded in that submodel. ...
arXiv:0801.0289v1
fatcat:7mwcyjmw75fppmgkjpzshxyapi
Review of Algorithmic Randomness and Complexity by Downey and Hirschfeldt
2013
ACM SIGACT News
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
In terms of Kolmogorov complexity and computability theory, one might say that highly random sequences contain a lot of information but not much useful information. ...
Downey and Hirschfeldt examine other topics as well, such as Kummer's Gap Theorem on the Kolmogorov complexity of c.e sets, and his theorem that the set of Kolmogorov random strings are truth-table complete ...
doi:10.1145/2447712.2447721
fatcat:ruecbllbf5d6nlwnglakqwb7zy
IS RANDOMNESS "NATIVE" TO COMPUTER SCIENCE?
[chapter]
2004
Current Trends in Theoretical Computer Science
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is application/pdf.
The best reference to the subject is Li-Vitanyi's book [29] (caution: they denote C, K what is here -and in most papers -denoted K, H). ...
Such Borel sets are, in fact, coded in any inner submodel of set theory. -Solovay random reals over a submodel of set theory are reals outside every measure zero Borel set coded in that submodel. ...
The Invariance Theorem A: Now, comes the fundamental result of the theory. We shall state it uniquely for Kolmogorov complexity but it also holds for conditional Kolmogorov complexity. ...
doi:10.1142/9789812562494_0046
fatcat:cwz6prus4ndwndcmi7zr4mbr7a
On hausdorff and topological dimensions of the kolmogorov complexity of the real line
1994
Journal of computer and system sciences (Print)
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2019; you can also visit the original URL.
The file type is application/pdf.
We investigate the Kolmogorov complexity of real numbers. Let K be the Kolmogorov complexity function; we determine the Hausdorff dimension and the topological dimension of the graph of K. ...
Since these dimensions are different, the graph of the Kolmogorov complexity function of the real line forms a fractal in the sense of Mandelbrot. ...
We thank Professors Allen Back, David Henderson, and Tom Rishel for interesting discussions on dimension theory and analysis. ...
doi:10.1016/s0022-0000(05)80073-x
fatcat:vgmphpoc6nc4xhwatn3glv2qkq
Computational power of neural networks: a characterization in terms of Kolmogorov complexity
1997
IEEE Transactions on Information Theory
Preserved Fulltext
A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2016; you can also visit the original URL.
The file type is application/pdf.
The computational power of recurrent neural networks is shown to depend ultimately on the complexity of the real constants (weights) of the network. ...
The complexity, or information contents, of the weights is measured by a variant of resource-bounded Kolmogorov complexity, taking into account the time required for constructing the numbers. ...
ACKNOWLEDGMENT The authors wish to thank E. Sontag for his encouragement and support via many discussions and D. Harel for asking the question that led them to Corollary 5.4. ...
doi:10.1109/18.605580
fatcat:bbpev5jiqrh4xhofiaygqtw55q
« Previous
Showing results 1 — 15 out of 35,804 results