How to find a word guaranteed not to be in a set?

Question

Algorithms

There is a certain alphabet - for example, A..Z.
There is a set of words from this alphabet.
Come up with a word from this alphabet that meets two requirements.
1. Not very long.
2. Not included in the set.
What are the considerations?

Answer 1

Figured it out, stupidly. Using combinatorics, we calculate how long (according to the Dirichlet principle) our word should be: for example, if we have numbers from 0 to 9 and 125 lines, it is enough to take three-digit ones. Here we take 126 bits (well, or 128 for a round count), from our numbers we take only three-digit ones and start filling in the bits. There is, for example, 025 - here in the 25th bit we put one. After that, it remains to find zero in the bit mask and convert it to our string: in the 45th place, it means 045.

Answer 2

https://en.wikipedia.org/wiki/Bloom_Filter

is a probabilistic data structure invented by Burton Bloom in 1970 that allows you to check whether an element belongs to a set. In this case, it is possible to get a false positive (there is no element in the set, but the data structure reports that it is), but not a false negative.