dictomaton VS PSI

Say you want to compute all strings of length 5 that the automaton can generate. Conceptually the nicest way is to create an automaton that matches any five characters and then compute the intersection between that automaton and the regex automaton. Then you can generate all the strings in the intersection automaton. Of course, IRL, you wouldn't actually generate the intersection (you can easily do this on the fly), but you get the idea.

Automata are really a lost art in modern natural language processing. We used to do things like store a large vocabulary in an deterministic acyclic minimized automaton (nice and compact, so-called dictionary automaton). And then to find, say all words within Levenshtein distance 2 of hacker, create a Levenshtein automaton for hacker and then compute (on the fly) the intersection between the Levenshtein automaton and the dictionary automaton. The language of the automaton is then all words within the intersection automaton.

I wrote a Java package a decade ago that implements some of this stuff:

https://github.com/danieldk/dictomaton

Also related: Levenshtein automata - automata for words that match every word within a given Levenshtein distance. The intersection of a Levenshtein automaton of a word and a DAWG gives you an automaton of all words within the given edit distance.

I haven't done any Java in years, but I made a Java package in 2013 that supports: DAWGs, Levenshtein automata and perfect hash automata:

https://github.com/danieldk/dictomaton

There are other techniques that aren't generally included in the "Zero Knowledge Proofs" set of techniques that are perhaps more practical for general development.

For example, I fine private set intersection[1] as implemented by OpenMined a really useful primative a bunch of privacy enhancing applications can be built on top of.

My colleagues and I recently published a pre-print[2] showing how to use this for sharing locations you and another person have had in common, without being able to see other locations. The paper talks about a social network built around this but I also think there are useful applications in things like real-world games (scavenger hunts etc)

[1] https://github.com/OpenMined/PSI/blob/master/private_set_int...

[2] https://arxiv.org/abs/2210.01927

I came here to say Golomb compressed sets except now I see it's part of the question!

They are used by default in the OpenMined implementation of Private Set Intersection[1] - a multi-party computation technique.

[1] https://github.com/OpenMined/PSI/blob/master/private_set_int...

I was using OpenMinded/PSI exploring some PSI implementations, but I would like a way for the server to know the intersection size. Say Signal wants to calculate the average number of users from one person's address book (or whatever).