The strategy this engine uses is just to evolve the state as a function of time. A match can be successfully completed, yet not be emitted because some other longer match could still supercede it by being longer or more leftmost.
I tried the pattern /d+s+/g on 10,000,000 digits followed by no space. It took 4 seconds to return no results. I tried it on 20,000,000 digits followed by no space. It took 8 seconds to return no results. I tried on 100,000,000 and I ran out of heap space.
Test setup: https://gist.github.com/conartist6/051838025af1e04d966e03aa9...
It's only when you return multiple matches that the engines have a problem and become superlinear.
For example in the expression in your example (I'm assuming based on your description of the test data that /d+s+/ means the same as /\d+\s+/ in the RE engines I've used) any match must contain a digit followed by a space.
A scan for all places where a digit is followed by whitespace with each such place then being checked to find the length of the string of whitespace starting there and the length of the string of digits ending there should be linear time and constant heap space.
https://memgraph.com/docs/querying/query-plan
The reason why I was looking was to do query planning for a declarative pattern-finding in atomic structures (hierarchical labelled graphs, I suppose) although I'm slowly realising just how insanely hard it might be to get it to work efficiently!
In a real-world deployment where you want to run any arbitrary regex in an idiot/malice-proof manner, the best solution is the same solution you'd use for running any other kind of untrusted code - sandbox it! A good regex API should limit its execution time and memory consumption and return a timeout error in case those limits are exceeded. Ideally, those parameters would be configurable at the API level. Unfortunately, the only regex libraries I know of that get this right are .NET's standard library Regex API and the third-party regex package in Python.
Here's your answer.
>Traditional regex is what came before it
No, that's "ancient regex".
wouldn't the "ancient regex" be the ed "g/re/p" version?
-E, --extended-regexp
Interpret PATTERNS as extended regular expressions (EREs, see below).
-G, --basic-regexp
Interpret PATTERNS as basic regular expressions (BREs, see below). This is the default.
-P, --perl-regexp
Interpret I<PATTERNS> as Perl-compatible regular expressions (PCREs). This option is experimental when combined with the -z (--null-data) option, and grep -P may warn of unimplemented features.
It seems that Boost actually uses 'perlex' https://www.boost.org/doc/libs/1_31_0/libs/regex/doc/syntax_... .
Ah, there is a post with more detail about RE# and discussion here recently that I must have missed: https://news.ycombinator.com/item?id=47206647
But if PCRE semantics isn't set in stone then i hope leftmost longest could be the default some day. There's a lot of nice things you get for free with the two pass approach
I would say that regexes that matter in practice, e.g. when digging through logs, have clear boundaries that curb the pathological backtracking behavior. In particular, I find it difficult to imagine a practical need to find all matches of an expression like /.*a|b/, as shown in the article. Realistically you'd have to handle /\b.*a|b\b/, or similar, because realistically when you need all matches, you don't want intersecting matches. This means you want to proceed past the end of the n-th match to look for n+1-th match, and never want to use indeterminate prefixes like /.*a/.
This OTOH gives a reasonably useful heuristic if your regexp comes from an untrusted source and could be adversarial. Check that it does not start with a prefix with a Kleene star, like /a*/. Require at least one positive match (in each alternate branch). Of course, /a+b|c/ would still be quadratic if your text is long sequences of "a" interspersed with characters other than "b". But this, again, is more of a theoretical case, to my mind.
I agree with you in the sense that most practical regexes do not expose this quadratic blowup (from all matches) but i do not think the same about backtracking. The effect of backtracking is immediately clear when you're searching inside text without a clear anchor like \A or ^ or a very rare string prefix. It is much more visible with either larger patterns or larger character classes like unicode
Greedy globs plus unanchored branches can turn a boring batch job into a CPU bonfire, and defensive limits seems a lot less optional when one dumb pattern can pin a core for minutes. A timeout or a restricted regex subset is usually cheaper than pretending everybody writes sane patterns.
there are many reasons to exploit things. one example is local privilege escalation. If your service has high privileges and somehow someone can edit an input source for it (like some file it reads thats accessible to the user, or even by tricking the service into looking at the wrong file) it will still be a useful vector.
now this might seem far fetched, but a lot of exploits i've seen actually do this type of stuff.
for example you find a program which gatheres some debug or support info package, and touches a directory which is user accessible. user put some kind of link or tricky file in there and boom, service compromised.
I would only not use hardened mode if the regex is actually embedded directly into the program, because that would atleast require the program itself to be touched before it breaks (which would already require the same level of privileges as the program runs on).
So, long story short. Be aware that if your program touches local resources that are not matching its own privilege level, like some log locations, tmp, etc , be sure that stuff doesn not get turned into regex or use the hardened mode to prevent problems.
its not always about users providing some input via an webpage or some online service that causes something to break..
- The Austin Group has recently accepted lazy quantifiers for inclusion into the next release of POSIX[1]. They think they have worked out a reasonable declarative definition for what they should mean. I am less than sure of that, but either way dismissing the whole thing as irredeemably tied to backtracking seems inappropriate.
- Once again the generalization in the title is AFAIK largely correct for industrial engines, but incorrect—arguably to the point of being misleading—for academic work. Just looking into the “parsing” subfolder of my papers stash reveals a 1998 paper[2] on linear-time maximal-munch tokenization, so at the very least the problem was recognized, and IIRC there’s a bunch of related work around that paper too.
- It is true that you can’t stream the haystack in the general case, but to what precise extent you can is an interesting question with a known algorithmic answer[3].
[1] https://www.austingroupbugs.net/view.php?id=793, https://www.austingroupbugs.net/view.php?id=1329, https://www.austingroupbugs.net/view.php?id=1857, see also the mailing list.
[2] Reps (1998), ACM TOPLAS 20(2), 259–273, https://dl.acm.org/doi/10.1145/276393.276394, https://research.cs.wisc.edu/wpis/papers/toplas98b.pdf.
[3] Grathwohl, Henglein, Rasmussen (2014), ICTAC ’14, LNCS 8687, 224–240, https://link.springer.com/chapter/10.1007/978-3-319-10882-7_..., https://utr.dk/pubs/files/grathwohl2014-0-paper.pdf.
That is surprising!
We've found that in certain simpler scenarios it's possible to use complement to express lazy quantifiers, but in the general case it appears very fragile.
a simple example: a.*?b can be rewritten to something like (a.*b&~(a.*b_+)) in RE# syntax, which effectively means "there is a match, but must not contain a shorter match"
> 1998 TOPLAS
I will read through it properly, but i can already see from page 8 that it requires a table of (DFA size x input length) which makes me very suspicious that it is more of a thought exercise than a real world solution.
> It is true that you can’t stream the haystack in the general case, but to what precise extent you can is an interesting question with a known algorithmic answer[3].
Thank you for this, this is an interesting paper
> That is surprising!
I mean, POSIX BREs (only!) also include (single-digit) backreferences. Surprisingly, (with such a restriction) this is actually polynomial[1,2] if impractical (h/t 'burntsushi for the reference[3]). But I still wouldn’t take POSIX as the arbiter of sanity in this case. Thus far I’m not even convinced their text actually amounts to a well-defined ordering on parse trees.
I don’t know if nongreedy quantifiers are all that interesting without match groups, though, so this isn’t a particularly burning question in my view.
[1] https://branchfree.org/2019/04/04/question-is-matching-fixed...
Here's the caveats.
And so running a regex engine on the matches seems like it would get you back to O(regexlen * haystacklen * matchcount) or roughly O(mn²) again.
Since a regex with ^<pattern>$ can not have overlapping matches it should guarantee linearity, given a linear engine. Or in the case of preprocessing lines first and then running is_match it's also linear
[0]: https://github.com/BurntSushi/rebar/pull/20#issuecomment-256...
Bringing a fully general CFG parser to parse regexps would be like hunting mosquitos with a nuke though..
I would argue that hardened mode should be default though, similar to how siphash is the default hashing function in Rust hash maps. Faster mode should be opt in if the user is confident that the supplied data is nonmalicious and they need the speed up.
Going forward this and the extended operators + large pattern perf will hopefully be a strong selling point to gain more traction
Wait, what? I thought this was about finding all matches. With a minor tweak to the opening example:
We want to match `(.*a | b)` against `bbbbbabbbbb`.
I want to detect each `b` individually, and I also want to detect `bbbbba`, `bbbba`, `bbba`, `bba`, `ba`, and `a`. That's what it means to find all matches.
Well, you changed the sentence I quoted. That doesn't really address what I was objecting to; I quoted that sentence because that's the first point in the essay where it's clear that you don't mean "all matches". That's where the reader becomes confused, but they don't become confused because that sentence is unclear - they become confused because everything else on the page is misleading, and that sentence unambiguously contradicts the misleading impression created by everything else.
Your headline says "all matches", your subheadline says "all matches", and your text both before and (still) after the sentence you changed frequently says "all matches", and in none of those cases do you actually mean "all matches". You mention that there is an existing solution, REmatch, but only to dismiss it as "solving a different problem", the problem of finding all matches. You also note that "all matches" is inherently quadratic because the size of the output is potentially quadratic, leading me to wonder why it's a surprise that asking for all matches yields quadratic performance.
The post states clearly "finding all leftmost-longest non-overlapping matches without quadratic blowup"
The engines mentioned at the beginning all return nonoverlapping matches. Basic document search returns nonoverlapping matches.
Finding overlapping matches is exotic and rarely ever used in practice outside of network security. It does solve a different problem
Jesus Christ, 80 hours?! I really hope the author seriously takes a proper break! I mean, they seem to be riding that incredible high that comes from having a breakthrough in deeply understanding a really tough problem after thinking about it for too long, so I kind of get it, but that is also all the more reason to take good care the precious brain that now stores all that knowledge, before it burns out!
Here's Kleene's Representation of Events in Nerve Nets and Finite Automata:
https://www.rand.org/content/dam/rand/pubs/research_memorand...
Most of this is about quadratic time find-all operations where a search operation is linear. But it's also still possible to get quadratic behaviour out of a single search without catastrophic backtracking, more easily than you might expect. In late January to early February, Tim Peters was talking about an example of this on the Python forums (see e.g. https://discuss.python.org/t/add-re-prefixmatch-deprecate-re...) and also related the experience of trying to diagnose the issue with AI (see https://discuss.python.org/t/claude-code-how-much-hype-how-m... and onward). Peters' example was:
\d+\s+
(This is arguably "backtracking" since it tries the longest match first, but clearly not in a catastrophic way; if you use `\d+?` instead then of course it only searches forward but is still O(n). It actually is slower in my testing in the Python implementation; I don't exactly know why. As noted in the discussion, the possessive quantifier `\d++` is considerably faster, and of course doesn't backtrack, but still causes O(n^2) searching. The repeated attempts to match `\s+` aren't the problem; the problem is repeatedly looking for digits in places where digits were already found and rejected.)
The way to fix this proposed in the discussion is to use a negative lookbehind assertion before the digits: `(?<!\d)\d+\s+`. This way, the regex engine can bail out early when it's in the middle of a digit string; if the previous character was a digit, then either `\d+\s+` doesn't match here, or it would have matched there.
A simpler idea is to just search for `\d\s+`, or even `\d\s` — since these will be present if and only if `\d+\s+` is. This way, though, you still need to do extra work with the partial match to identify the start and end of the full match. My first idea was to use positive lookbehind for the digits, since the lookbehind match doesn't need to backtrack. In fact lookbehinds require a fixed-length pattern, so this is really just a more complicated way to do the `\d\s+` simplification.
----
> Hyperscan (and its fork Vectorscan) is a true linear-time all-matches regex engine. it achieves this by using "earliest match" semantics - reporting a match the moment the DFA enters a match state, instead of continuing to find the longest one.
Is this not just equivalent to forcing "reluctant" quantifiers (`\d+?`) everywhere?
Just a small note: some regex engines support "variable length lookbehind", check the last column on this wikipedia article : https://en.wikipedia.org/wiki/Comparison_of_regular_expressi...
eg. /abc*/ and abccccc will return you matches at ab|c|c|c|c|c|
I think it's very common and ok that people reason about other engines in terms of backtracking but it works very differently. And fixed length lookbehinds are more of a Java/Python thing, other engines support all lookbehinds.
The main idea of linear regex and intuitive semantics is that it should be declarative and the engine does whatever is the fastest without you having to worry about it. Instead of describing character by character how to perform the search and where it can blow up, think of it as just a specification. Then you can truly express whatever is the shortest/most convenient to explain.
Something i'm still trying to figure out and perhaps failing to understand is what are the killer features of backtracking regex that you would really miss if you were to use linear regex? It would help me a lot to know, i'm trying to convince others to make the switch
The problem is that this is one of the regexes that backtracking engines have a bad time with.
With a NFA implementation it can be done in O(regexlen * haystacklen) time, though that only holds for true regular expressions (no backreferences).
https://swtch.com/~rsc/regexp/regexp1.html
And then for re.search, since the NFA wants to just do it once, it should run it with the pattern as
^.*?(\d+\s+).*$
Jack Dorsey's layoff message last month did the same thing.
Is it some kind of "Prove you're not an AI by purposely writing like an idiot" or something?
I keep being surprised by the magnitude of the disconnect between this place and the other circles of hell. I'd have thought the Venn diagram would have a lot more overlap.
The confusion might be understandable for people who have never encountered this style before, but that's still a very uncharitable take about an otherwise pretty interesting article.
By the way, I consider it a pretty disgraceful defect of HN that people routinely "flag" opinions merely because they disagree. The flag is for spam, not for downvoting.
It reminds me of how peer review is supposed to be blind, but certain authors like Simon Peyton Jones have such a distinctive voice that surely reviewers instantly know when a paper is by him. The models have been successfully made to talk in a particular way, and it's very clear once you becomes familiar with it. My guess is that most HN users are not familiar and I just sound like a crazy person to them
The author admitted it in another comment anyway https://news.ycombinator.com/item?id=47494833
"Compiling regular expressions to sequential machines" (2005) ACM Symposium of Applied Computing https://dl.acm.org/doi/10.1145/1066677.1066992
(Note that there is a small mistake in the paper due to ambiguity, found by Vladimir Gapeyev. So the result does not hold in the generality stated but only for a special case when there is no ambiguity at "the end". There went my first PhD student publication...)
The two pass technique used to be implemented in the Scala compiler at the time (building DFAs upfront) , which could do regexps over lists and other sequences, but the approach would not work for top-down tree regexps so I did not pursue that and it got ripped out later.
It is good to see derivative regular expressions, Brzozowski/"position automata" used and discussed.