(06-09-2024, 09:47 PM)lelle wrote: You are not allowed to view links. Register or Login to view.Can anyone please explain what might be a reasonable underlying mechanism for the observed word length distribution in the VMs? The author flipping 9 (or 10) coins simultaneously and counting numbers of heads. Numbers of heads will then dictate the length of the current word?
Coin toss as a model for the letters of a word ( as I understood it ):
The binomial distribution only knows two "states": success or failure.
With n = 9, a coin is therefore tossed 9 times in succession, with heads standing for success and numbers for failure.
Each coin toss is seen as a decision as to whether another letter is added to the word.
On each of the "n" (here 9 or 10) tosses, the coin (or the probability "p", here symmetrical 0.5) influences how long the word becomes.
"Heads" could mean, for example, that a letter is added.
"Number" could mean that no further letter is added.
The binomial distribution then models the probability of how many letters are contained in a word at the end of such a process.
Stolfi`s "Shifted by 1" means that the actual word length does not range from 0 to 9, but from 1 to 10. Each value from the binomial distribution is therefore increased by 1. A word with a length of 0 should not occur.
In my code, as soon as the target word length has been determined, the words are shortened or lengthened accordingly.