Over christmas we had a look at the GCHQ christmas quiz [1]. The idea is that you solve a set of small puzzles, each producing a letter, which then become labels of the nodes of a directed graph, and you have to find a Eulerian path through the graph (visiting some nodes multiple times) which spells out a festive word or phrase.

We solved two or three of the small puzzles, but couldn't get the rest. I wondered if we could solve the overall puzzle without knowing the letters, by exploiting the structure of the graph: perhaps there are simply not many words or phases which could be produced by the graph.

Enumerating the possible paths through the graph was straightforward (there are a few hundred, i think). Matching those paths against individual words, if you have a word list, is easy. But where i was stumped was matching them against phrases containing multiple words. Trying every possible sequence of words, even lazily assembled, felt like it would be a combinatorial explosion that i would never be able to get through.

Using a corpus of phrases from wikipedia is absolute genius.

[1] https://www.gchq.gov.uk/news/christmas-card-2020 - note that the edge with a double arrow is really two edges, one in each direction

That's the first time I see a regular expression implementation with intersection, apart from my own from many, many moons ago. A pleasant surprise. I also had added a negation operator, which adds another level of unintuitive behavior. E.g., you might think that !a would block aa from matching, but it doesn't.

The anagram operator is a new one for me. Nice.

I've once implemented a regular expression engine based directly on https://en.wikipedia.org/wiki/Brzozowski_derivative – it's straightforward to implement both intersection and negation this way.

hfst (open source rewrite of the Xerox finite state toolkit) includes negation:

    $ echo 'a b
    c b
    c d*' | hfst-regexp2fst > ab.fst
    $ echo 'c ?+' | hfst-regexp2fst >cdotplus.fst
    $ hfst-intersect ab.fst cdotplus.fst | hfst-expand -c3
    cb
    cd
    cdd
    cddd
    cdddd
    $ hfst-expand -c3 ab.fst
    ab
    cb
    c
    cd
    cdd
    cddd
    

The regex syntax is a bit quirky due to backwards compatibility with lexicons written in XFST, see https://github.com/hfst/hfst/wiki/Regular-Expression-Operato...