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https://issues.apache.org/jira/browse/LUCENE-10010?page=com.atlassian.jira.plugin.system.issuetabpanels:comment-tabpanel&focusedCommentId=17381092#comment-17381092
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Dawid Weiss commented on LUCENE-10010:
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bq. As far as I understand (which might be wrong), the way we're currently use
DFA to intersect with term dictionary is to provide a initial term (which might
be null), then based on that term find the next acceptable term in
lexicographic order. I think this can still be done using an NFA?
Shouting from the sideline a bit but trying to help... I think this should be
doable, even with epsilon transitions, etc. The difference is that instead of a
single automaton state (prefix), you have to keep track of multiple states
currently being visited (prefixes) - if you keep these in a sorted order
(heap?) then you know exactly the next minimal prefix that has a chance to
match and scan/ skip the term index accordingly.
> Should we have a NFA Query?
> ---------------------------
>
> Key: LUCENE-10010
> URL: https://issues.apache.org/jira/browse/LUCENE-10010
> Project: Lucene - Core
> Issue Type: New Feature
> Components: core/search
> Affects Versions: main (9.0)
> Reporter: Haoyu Zhai
> Priority: Major
>
> Today when a {{RegexpQuery}} is created, it will be translated to NFA,
> determinized to DFA and eventually become an {{AutomatonQuery}}, which is
> very fast. However, not every NFA could be determinized to DFA easily, the
> example given in LUCENE-9981 showed how easy could a short regexp break the
> determinize process.
> Maybe, instead of marking those kind of queries as adversarial cases, we
> could make a new kind of NFA query, which execute directly on NFA and thus no
> need to worry about determinize process or determinized DFA size. It should
> be slower, but also makes those adversarial cases doable.
> [This article|https://swtch.com/~rsc/regexp/regexp1.html] has provided a
> simple but efficient way of searching over NFA, essentially it is a partial
> determinize process that only determinize the necessary part of DFA. Maybe we
> could give it a try?
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