26

Re: About one paradox of information entropy

FXS wrote:

a problem in how at such recoding to do without "the transfer dictionary", or with such dictionary which would not superimpose (the length) all effect of compression.

, in any way.

FXS wrote:

feel a dirty trick: it turns out that absolutely casual bit sequence is not compressed (though personally the hope) that in it is extreme a lot of information still decays!

Indeed.
In it is absolute casual sequence any element it is not reduced to remaining, therefore the information there is maximum.

27

Re: About one paradox of information entropy

FXS wrote:

Also there are good chances to hope that "scoring" (in a bit count) from this compression will be more than length bits of number designation . And even (it is possible, especially if N it is great) more than length bits of our algorithm  which has been written down on any "economical" byte-code...
It is possible to say explicitly, at last, that, knowing only , we always can repeatedly generate a line Z and, subtracting it from R, to receive initial S.

Most likely is not present. For achievement of such accuracy we should That-that  ours
Very precisely. Consider that calibration of initial parameter seed will cost so expensively as well as all
Your compressed sequence.

28

Re: About one paradox of information entropy

Barlone wrote:

No archiver compresses casual sequence.

To compress arbitrary (including "casual") a line S it is possible to (try), for example, so:
1. To find in it 2 (in words: two ) identical substrings Zi (Z1 and Z2), it is desirable more long;
2. In an output flow to write down at first three numbers: length Zi, Z1 address, Z2 address. Then - substring Zi. Then - a line S', representing S from which are thrown out Z1 and Z2.
How you consider, it is very rare situation and the difficult task? For enough long and enough casual line S - whether the probability is very great, what it will not be possible to find in it Z1 and Z2 such, what the length Zi is more than the length necessary to allocate three numbers?

29

Re: About one paradox of information entropy

FXS wrote:

And prefix coding, for example, specially is engaged in that aligns (as it is possible is better) frequencies of words. With the registration of lengths, it is finite: all words in length of 8 bits should have frequencies, in an ideal, equal 1/256; and words in length of 10 bits - equal 1/1024...

Prefix coding rough enough. Especially on frequent values (there where  a tree
Displaces in leaves on short branches). If to take the English text (where it is already counted
Density of compression in 2 bits on the character) and to apply to it  or shennona-fano
You of expected 25 % do not receive that.
In an ideal for the frequency compression use the arithmetical coder (as in Winrar) but I suspect
That  the good text archiver has a whole pipeline of methods. And arithmetics
It simply part of this stack which slightly refines entropy.

30

Re: About one paradox of information entropy

mayton;
What is "accuracy of parametrization" ? Also what such calibration of initial parameter seed?
Unless we speak about  on the base of "thermal noise" (any crystal), instead of about algorithmic  (which it is absolutely determined, for an essence algorithm)?

31

Re: About one paradox of information entropy

FXS wrote:

As you consider, it is very rare situation and the difficult task? For enough long and enough casual line S - whether the probability is very great, what it will not be possible to find in it Z1 and Z2 such, what the length Zi is more than the length necessary to allocate three numbers?

(I am sorry. I answer on a topic and from below simultaneously).
I think that here the task is similar to the transport. We will probably stand in a choice condition.
We found 3 sequences on 5 bits. And 5 sequences on 3 bits. And generally...
We not in a state to predict as the initial sequence will look
AFTER we already drew in it. Probably there will be chains of bits which again
It is possible to draw in etc. And probably it is necessary to return recursively back and to take 2 bits on 7. And still
Time...
it is the task  difficult. Also that is insulting - while without perspective to quit on any
The guaranteed result.
P.S. Small but on three roubles
Big on five roubles
() the Novel Kartsev

32

Re: About one paradox of information entropy

FXS wrote:

mayton;
What is "accuracy of parametrization" ? Also what such calibration of initial parameter seed?
Unless we speak about  on the base of "thermal noise" (any crystal), instead of about algorithmic  (which it is absolutely determined, for an essence algorithm)?

All is true. I mean pseudo-casual .

33

Re: About one paradox of information entropy

mayton wrote:

We not in a state to predict as the initial sequence will look
AFTER we already drew in it.

Why "not in a state to predict" if we produce with it the formal operations?
The example is Perhaps necessary? Here "casual" sequence (slightly , yes):
JHDBCEBVJEGGB ABCD KJFDBNCDKMNEJLLCMVPW ABCD ELHLMAKSHFIHJKDPPWL
Here it "compressed":
4 1 2 ABCD JHDBCEBVJEGGB KJFDBNCDKMNEJLLCMVPW ELHLMAKSHFIHJKDPPWL

mayton wrote:

we will Probably stand in a choice condition.
We found 3 sequences on 5 bits. And 5 sequences on 3 bits.

We can consider that to us it is more favourable, and we can, not , to take "on 5". And for demonstration of the basic possibility of compression enough single-valued substring repetitions.

34

Re: About one paradox of information entropy

Dima T wrote:

Ivan FXS, I here that thought: if you are right, i.e. your idea the worker it is possible to press everything indefinitely. Well at least in tens times. For example the distribution kit  to compress to 1 MB, let even 100 MB, I think for the sake of it MS would launch search for couple of months.
Output: if it worked, it already would use.

I over it thought for a long time. Also came to the concept of the ideal archiver of the text.
I considered three levels.
Level of [/b characters (arithmetics, , PPM) already all  up and down.
[b] Level of syllables
(LZW), words, (Dictionaries). Too it is researched. The Archiver-directory already entered in
and  as a joke.
Level of sentences (sentences). Here - it is not known. Nobody knows as they are under construction.
More truly there is a dial-up . But how to describe creative flight ? I thought. And also it is not necessary.
Sentences even in Russian are under construction on a certain template. I have enough
To analyze texts of one author. And to construct on them Markov models (MM). Roughly...
It looks as FSM at which passages have probabilities. Thus the MM output is
Template generation sentences with a binding to previous sentence.
I state that for text generation on my model to me to do control signals enough
For given in MM. Thus signals will be compressed owing to entropy certainly known to me.
Still which I for myself did not solve a question - what size will be the description of MM together
With structure of passages.
Other levels. Styles. Parts. Heads. . The model should include other models recursively.
For example any narration contains passages from one literary style to another.

35

Re: About one paradox of information entropy

FXS wrote:

why "not in a state to predict" if we produce with it the formal operations?
The example is Perhaps necessary? Here "casual" sequence (slightly , yes):
JHDBCEBVJEGGB ABCD KJFDBNCDKMNEJLLCMVPW ABCD ELHLMAKSHFIHJKDPPWL
Here it "compressed":
4 1 2 ABCD JHDBCEBVJEGGB KJFDBNCDKMNEJLLCMVPW ELHLMAKSHFIHJKDPPWL

It not is the forecast. In the first you - artificially simplified the initial data. Instead of bits - characters.
In the second - you  alphabetic sequence. smile)) Give me bits and white noise.
But let's distract. In the adjacent topic two "pepper" argue 2 months on the task of arrangement of 8 queens.
I even lost a thread of their dialogue and I do not know about what it. Fractals, Germans any congresses... Well  with it.
... This task was solved still by the Gauss. He would search for the analytical (formular) decision which gave at once
(Instantly) the answer. As a matter of fact he wanted O (1) formula. And it is not present. The matter is that all combinatorial tasks
And chess including has no formular decision. They are recursive by the nature and we cannot
To make a position estimation yet we do not make a position estimation.... While... And so on to a checkmate.
I consider that the given task (namely the estimation of efficiency of compression after application of changeovers) - is recursive.

36

Re: About one paradox of information entropy

mayton wrote:

a place of bits - [/quote characters everything that there is in a computer, a bit essence.

mayton wrote:

Give to me... White noise.

where I it will take - here and now?!

mayton wrote:

artificially simplified the initial data

Generally, I now polemized with the statement: "no archiver compresses casual sequence", and even I slightly  - to "any archiver any casual sequence never in any way compresses it". Also showed that quite trivial archiver can somehow sometimes compress some casual sequences.

37

Re: About one paradox of information entropy

FXS wrote:

everything that there is in a computer, a bit essence.

Oh the sly fellow...

mayton wrote:

where I it will take - here and now?!

Linux is? On  ?

38

Re: About one paradox of information entropy

Still I will throw  over which thought. If to take bit sequence in length N
And cyclicalally to shift it on 1 bit and  on the unit two with original that
We receive a card of differences.
If we continue cyclical rotation N of times that we receive N variants of differences.
And if we select that difference where the amount of zero bits will be maximum - that more likely
In total we found big bit under-sequence which some times meets
In the original. Self-similarity or a fractal.
Further - a trick. We select the longest sequences of zero in a difference and it is solved;
To add them in the reference manual of the archiver or not.

39

Re: About one paradox of information entropy

FXS wrote:

it is passed...
To compress arbitrary (including "casual") a line S it is possible to (try), for example, so:
1. To find in it 2 (in words: two ) identical substrings Zi (Z1 and Z2), it is desirable more long;
2. In an output flow to write down at first three numbers: length Zi, Z1 address, Z2 address. Then - substring Zi. Then - a line S', representing S from which are thrown out Z1 and Z2.
How you consider, it is very rare situation and the difficult task? For enough long and enough casual line S - whether the probability is very great, what it will not be possible to find in it Z1 and Z2 such, what the length Zi is more than the length necessary to allocate three numbers?

Well archivers approximately and work. So simply check up. Here to you 16 casual sequence, compress.

#include <stdio.h>
#include <stdlib.h>
int main () {
int i;
unsigned char n;
FILE *f;
f = fopen ("rand.dat", "wb");
for (i=0; i <16777216; ++ i)
{
n=rand ()>> 7;
fwrite (&n,1,1,f);
}
fclose (f);
return 0;
}

40

Re: About one paradox of information entropy

FXS wrote:

Generally, I now polemized with the statement: "no archiver compresses casual sequence", and even I slightly  - to "any archiver any casual sequence never in any way compresses it". Also showed that quite trivial archiver can somehow sometimes compress some casual sequences.

Well so it is possible to understand randomness on a miscellaneous. It is finite casual sequence can to begin with pair of hundreds zero bits absolutely casually.
Or so https://xkcd.com/221/

41

Re: About one paradox of information entropy

Here from ours CardRaytracer. The linear congruent.
Constants M, J not the unique.
The casting in double can be thrown out .

static final int M = 1_048_576;//2^20
static final int J = 2_045;
int oldI = 12357;
double Random () {
oldI = (oldI * J + 1) % M;
return (double) oldI / M;
}

42

Re: About one paradox of information entropy

Barlone wrote:

It is finite casual sequence can to begin with pair of hundreds zero bits absolutely casually.

yes, whether therefore a question "the archiver compresses casual sequence?" It is necessary to understand or as
"Whether the archiver compresses any casual sequence at least on 1 bit?"
Or as
"What mathematical expectation of value of compression by the archiver of casual sequence (with understanding of what it at all does not compress some)?"
For mathematical estimations show that, yes, tanks fly, but nizenko-nizenko...

43

Re: About one paradox of information entropy

FXS wrote:

yes, whether therefore a question "the archiver compresses casual sequence?" It is necessary to understand or as
"Whether the archiver compresses any casual sequence at least on 1 bit?"
Or as
"What mathematical expectation of value of compression by the archiver of casual sequence (with understanding of what it at all does not compress some)?"
For mathematical estimations show that, yes, tanks fly, but nizenko-nizenko...

Well if to consider that in case of failure of compression the archiver should add a minimum of 1 bit - a sign "is not compressed", for the ideal archiver  values of compression will be zero, and for imperfect - negative.

44

Re: About one paradox of information entropy

Barlone wrote:

Here to you 16 casual sequence, compress....

It can be compressed

https://ru.wikipedia.org/wiki/__#_ wrote:

the Length of cycles  depends on the generator and makes nearby 2 ^ (n/2) though linear congruent and RSLOS-GENERATORS possess the maximum cycles of the order 2^n where n - the size of internal state in bits

Nobody knows what cycle at it  it turns out. For 32-bit the cycle from 65536 can be.

45

Re: About one paradox of information entropy

FXS wrote:

And as it is connected "" to arguing of comparative compressibility (a pliability to compression) lines (messages) of type resulted by you

Ivan, do not carp, at me a habit to answer the adjacent questions as you too juggle, happens, terms "with ease unusual".
It is connected, that it was remembered or caused arguing. The message presumably encoded exactly one bit of the information intended for the Customer (true). The distorted phrase as a result "" gives our way NULL, those , i.e. absence expected  for the Customer, and it is necessary to repeat transmission. Both there, and there 1 bit, and lengths of the files which have left in an ether, different was encoded. The idea of an example was in it. It agree that  lines are not so indicative.
The information for the Customer - consisted in it mine . Unlike the information for a communication channel, as a matter of fact - from length of a transmittable file. And, by the way, if to sign ', the line after all is extended? (It is admissible, I signed simply from  instead of to certify myself)
I repeat, talks about  - while it is all .

46

Re: About one paradox of information entropy

exp98;
All the same I see some difference between a situation when the sender has a packing (compressing) algorithm, and at the receiver - corresponding to it (to packing algorithm) unpacking algorithm; generally speaking, the arbitrary messages also go...
And a situation when the sender purposefully builds the messages as citations (paragraphs) of literary classics, and messages sends in a type (a name of the author; volume number; page; paragraph number).

47

Re: About one paradox of information entropy

Dima T wrote:

it is passed...
It can be compressed
it is passed...
Nobody knows what cycle at it  it turns out. For 32-bit the cycle from 65536 can be.

Yes, in an amicable way certainly it is necessary  to use "correct". And so on implementation in the compiler depends.

48

Re: About one paradox of information entropy

Dima T wrote:

Nobody knows what cycle at it  it turns out. For 32-bit the cycle from 65536 can be.

- "for specific value seed" it is necessary to add.

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