21–30 of 102 posts
I am currently transitioning to a different blog engine, so the page is offline right now, but it's still available here
https://web.archive.org/web/20220513113609/neilk.net/blog/20...
https://metacpan.org/pod/Regexp::Exhaustive#Finding-all-divi...
And if you're in Toronto in 3 weeks time, come see Abigail (the original inventor of the prime number regexp) solve the N-Queens problem with regexp:
https://tprc2023.sched.com/event/1LhoB/the-n-queens-problem-...
Technically not a regular expression, as (intuitively) the backreference has to “count” the number of 1’s that were matched. Regular expressions are equivalent to finite state machines, which cannot count arbitrarily high (any state machine that can count arbitrarily high needs an infinite number of states, since there are infinite natural numbers). The 2022 discussion has a more formal proof using the pumping lemma.
> Regular expressions are equivalent to finite state machines, which cannot count arbitrarily high (any state machine that can count arbitrarily high needs an infinite number of states, since there are infinite natural numbers). The machine I'm using to type this comment is also a finite state machine, as due to having non-infinite memory, it also cannot count arbitrarily high. Informally, regular expressions like in…
I'm not sure how that's relevant. Even given infinite space, there still wouldn't exist a Regular Expression (the CS kind) you could write down in finite time that would match only primes.
At least IIRC, it's been a 20+ years since I last took a Discrete Math course :)
Technically not a regular expression, as (intuitively) the backreference has to “count” the number of 1’s that were matched. Regular expressions are equivalent to finite state machines, which cannot count arbitrarily high (any state machine that can count arbitrarily high needs an infinite number of states, since there are infinite natural numbers). The 2022 discussion has a more formal proof using the pumping lemma.
> Regular expressions are equivalent to finite state machines, which cannot count arbitrarily high (any state machine that can count arbitrarily high needs an infinite number of states, since there are infinite natural numbers). The machine I'm using to type this comment is also a finite state machine, as due to having non-infinite memory, it also cannot count arbitrarily high. Informally, regular expressions like in…
Right. And if you really want to push that argument further then there are numbers for which your machine can't decide whether they are prime or not. Most of them, in fact, i.e., for all but a finite number of primes and non-primes, your machine can't tell.
For the theory of computability, this is not a useful model. Neither for complexity theory. Statements like "My machine can sort in constant time" which is arguably true but not useful either. It only holds up to a certain collection size which in a sense makes it both nonsensical and useless. Even concepts like the Chomsky hierarchy with context free languages being one of the prominent components make little sense as long as your computational model is finite state.
Instead, we model them as unbounded, to be able to differentiate between classes of computation problems as well as reason about complexity. The Turing Machine is one of the simple and elegant models, but there are others for other purposes.
I wish that basic education about the theory of computation would stress more why theory treats things like this, to avoid this kind of confusion. (And then people would need to take those classes as well, and not just claim they can write React apps just fine without a degree.)
Earlier quoted context omitted.
> Regular expressions are equivalent to finite state machines, which cannot count arbitrarily high (any state machine that can count arbitrarily high needs an infinite number of states, since there are infinite natural numbers). The machine I'm using to type this comment is also a finite state machine, as due to having non-infinite memory, it also cannot count arbitrarily high. Informally, regular expressions like in…
> The machine I'm using to type this comment is also a finite state machine, as due to having non-infinite memory, it also cannot count arbitrarily high. I'm not sure how that's relevant. Even given infinite space, there still wouldn't exist a Regular Expression (the CS kind) you could write down in finite time that would match only primes. At least IIRC, it's been a 20+ years since I last took a Discrete Math course…
The point is, neither would there exist a non-(Regular Expression) method that could do such, if you're running it on a finite state machine (your computer).
Earlier quoted context omitted.
Agreed. I read the post because the result was so shocking. TIL that the computer-sciencey definition of RE isn't the only one in use.
When programmers say regular expression they usually mean Perl Compatible Regular Expressions (PCRE). Or I guess PCRE-compatible expressions, since there are other implementations of the same syntax out there. If you go back far enough in time they were once regular expressions in the computer science sense, but then features got added, and now they are incredibly powerful but can take basically infinite memory and t…
Which is why the "RE" in the article is excrutiatingly slow, given that it needs to perform insane amounts of backtracking. In contrast, "real" regular expression checkers run in linear time.
Also, nitpicking, but they take unbounded time. It's still finite.
Earlier quoted context omitted.
> The machine I'm using to type this comment is also a finite state machine, as due to having non-infinite memory, it also cannot count arbitrarily high. I'm not sure how that's relevant. Even given infinite space, there still wouldn't exist a Regular Expression (the CS kind) you could write down in finite time that would match only primes. At least IIRC, it's been a 20+ years since I last took a Discrete Math course…
> Even given infinite space, there still wouldn't exist a Regular Expression (the CS kind) you could write down in finite time that would match only primes. The point is, neither would there exist a non-(Regular Expression) method that could do such, if you're running it on a finite state machine (your computer).
It's more interesting to ask: suppose you did have a magical stick of RAM that had infinite storage, and suppose you augmented your computer to store and query that memory. Then -- yes -- your computer could determine whether any number, however large, is prime. An FSM could not.
It is validating whether a string of consecutive 1's has a prime length.
In other words, it can't tell whether "3" is prime, unless you express it as "111".
Much less exciting.
Earlier quoted context omitted.
> Even given infinite space, there still wouldn't exist a Regular Expression (the CS kind) you could write down in finite time that would match only primes. The point is, neither would there exist a non-(Regular Expression) method that could do such, if you're running it on a finite state machine (your computer).
But that argument is not interesting. "We can't count arbitrarily high because the universe is finite." Yeah, duh. (Observable universe, for the pedants.) It's more interesting to ask: suppose you did have a magical stick of RAM that had infinite storage, and suppose you augmented your computer to store and query that memory. Then -- yes -- your computer could determine whether any number, however large, is prime. An…