# Re: definition of statistical test for randomness

*From*: "Joseph Ashwood" <ashwood@xxxxxxx>*Date*: Sat, 03 Feb 2007 04:39:54 GMT

"asdf" <qjohnny2000@xxxxxxxxx> wrote in message

news:1170421318.473941.109440@xxxxxxxxxxxxxxxxxxxxxxxxxxxxxxx

Is there such a thing as a "valid" test for non-randomness - a

test that can be used to give you confidence.

No there isn't. The reason is very simple, in a true balanced coin flip

you

are just as likely to have

0000000000000000000000000000000000000000000000000000000000000000000000000000000

as

0101000110010101001001001110110100100100110110010010101001001001011010101010101

or

1111111111111111111111111111111111111111111111111111111111111111111111111111111

or any other pattern so no test on the output can ever test for

randomness.

- Suppose though that these 0's went on forever - then you could say

the string was not random.

No you couldn't, it is still a perfectly valid output from a random bit

generator.

- But if the number of 0's went above the number or 1's and below the

number of 1's an infinite amount

of times I'm not sure if this says the sequence is not random.

It means nothing compared to a perfect random bit generator.

Basically what I'm trying to figure out is why Martin-Lof definition

is a good definition for randomness of

infinite sequences.

It isn't. At best it is an attempt to quantify the apparent randomness of

the bit stream, this is radically different from the actual randomness of

the bit stream.

There simply cannot exist a test of actual randomness/entropy of a bit

stream. For apparent randomness/apparent entropy there are an infinite

number of them.

Joe

.

**Follow-Ups**:**Re: definition of statistical test for randomness***From:*Bryan Olson

**References**:**Re: definition of statistical test for randomness***From:*asdf

**Re: definition of statistical test for randomness***From:*Joseph Ashwood

**Re: definition of statistical test for randomness***From:*asdf

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