Have read that the complexity of #Bitcoin PoW function is "O(2^(log n) / n)" because number of nonces you need to try is relative to the number of nonces that give a difficulty less than difficulty you are currently at.
What that means & why it matters?
Could someone explain it to me ?
Yes, someone please explain this for everybody...
Nonce and for all.
Your joke is
I'll try to give a brief explanation.
First of all, the #bitcoin protocol is based on a data structure called a 'blockchain' (sequence of blocks of data).
Each block contains some information (usually a list of transactions), a reference to the previous block in the chain & a cryptographic hash of the data.
Thus, if you want to change a block, you must also change all the blocks that come after it, because changing a block changes its cryptographic hash, which changes the cryptographic hash of the next block, and so on.
The bitcoin protocol has a special rule: the block at the end of the chain must have a cryptographic hash that starts with a certain number of zeros (currently, 6).
This is why it's called 'mining’: you have to work very hard to find a block that has the right cryptographic hash.
The computational complexity of finding a block is 'O': the target is a '256-bit number'
If the number of miners doubles, then the probability of a given miner finding a block will only decrease by a factor of two. This is due to the fact that the difficulty will be increased to keep the average rate at which blocks are found the same.
The probability that a given 'nonce' produces a hash starting with a zero is therefore '1/2^(log n)' where 'n' is the number of leading zero bits required, so the probability of any given nonce producing a hash starting with 3 zeros is approximately 1/2^3 or 1/8.
If 'n' is the number of leading zero bits required then why is the probability 1/2^(log n) & not 1/2^(n) ?
I asked GPT-4
The statement you read is not entirely accurate. The complexity of Bitcoin's Proof of Work (PoW) function is not "O(2^(log n) / n)". Instead, the complexity of finding a valid PoW solution can be expressed as "O(2^k)", where "k" is the number of leading zeros required in the hash output, which is determined by the target difficulty.
O(): The big-O notation, which describes the upper bound of the growth rate of an algorithm. It is used to analyze and compare the efficiency of algorithms in terms of their time complexity or the number of operations they perform.
My statement is only a trick, 'fake chain' 'hypothesis' of a computational complexity of O(2^(log n)/n) for 'forging' a chain of length n, where n is the number of blocks in the chain. (A difficult task because the hash of each block in the chain is based on the previous block's hash, so changing any part of the chain would require recalculating the hashes for all subsequent blocks).
By the way, forging a chain refers to the act of creating a 'fraudulent chain' that appears to be legitimate.
I think O(2^(log n) / n) can be broken down as follows if you’re familiar with mathematics:
log n: Logarithm of n, which is the exponent to which 2 must be raised to obtain n. 2^(log n): Equivalent to n, since 2^(log n) = n. & 2^(log n) / n: will represent the ratio between the amount of work required & the size of the input.
"2^(log n)" is essentially another way of writing "n", because 2 raised to the power of log n gives you n. So you can think of this part as n/n, which simplifies to 1.
Consequently, the computational complexity can be simplified to O(1/n). This means that as the length of the chain (n) increases, the computational requirements for forging a chain increase, but not proportionally.
Specifically, the computational requirements decrease as the length of the chain increases.
Simply, it becomes exponentially more difficult to forge a longer chain, which is a desirable property for a 'secure cryptographic system' like #Bitcoin.
Charlatans are to the dozen, aren’t they?!
It could be… Not to be fooled again by those tricky charlatans..
Exploited you mean?
Perhaps….
Don’t think.
Somewhat insecure to argue that you’re doing it.
Down Ike a clown.
What? You are not cool enough to play with the cool kids?
I don’t.
Oh this?!
What’s the matter? The laundry service is a hush hush operation not doing good with users and marketing?
Kinda my prerogative, don’t you think, Mark? Sure wanna disco about it?!
#mv
In the apexness is it?!
Smell me a clown somehow.
Guess serving sin frowns upon doing stuff to us the way deviance does.
Not a better detergent than most too, you clown??!
Envy much?!
But hey, go faking the #nft market too.
#embarrassing and insulting to insinuate.
Not a social deviant are you, Mark?
But guess the lost in chaos haven’t really got a handle on temporal mechanics and those bits yet, to foresee those IRS changes to bitcoin legalities to close those corruption detergent when coining without unlicensed bit.
