Hard code golf: Regex for divisibility by 7

  • Matthias Goergens has a 25,604-character (down from the original 63,993-character) regex to match numbers divisible by 7, but that includes a lot of fluff: redundant parentheses, distribution (xx|xy|yx|yy rather than [xy]{2}) and other issues, though I'm sure a fresh start would be helpful in saving space. How small can this be made?



    Any reasonable variety of regular expressions are allowed, but no executable code in the regex.



    The regular expression should match all strings containing the decimal representation of a number divisible by 7 and no others. Extra credit for a regex that does not allow initial 0s.


    What is the precise intention? Does it have to match all numbers of any size divisible by 7, or, for example, only valid 32-bit uints?

    @Peter Taylor: It should match all strings that are the decimal representation of a number divisible by 7. Extra credit for solutions that disallow leading 0s.

    By any chance... need the regex *not match* numbers indivisible by 7?

    @boothby: Absolutely, else you could just use the empty expression.

    That leaves out Perl 6 as a Regex inherits from Method so is a form of executable code.

    Would you please clarify whether you want to allow the number zero in the case of no "initial 0s"?

    @n̴̖̋h̷͉̃a̷̭̿h̸̡̅ẗ̵̨́d̷̰̀ĥ̷̳ Yes, 0 should be allowed in either version.

  • 10791 characters, leading zeros allowed



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5)(6|43*5)*(0|7|43*6))|(2|9|46*4)(3|56*4)*(6|56*[07]))(4|36*[07]|(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))|(1|8|36*4)(3|56*4)*(6|56*[07]))*(5|36*[18]|(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(3|63*[07]|(1|8|63*5)(6|43*5)*(1|8|43*[07]))|(1|8|36*4)(3|56*4)*(0|7|56*[18])))(2|9|53*[07]|(0|7|53*5)(6|43*5)*(1|8|43*[07])|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(5|36*[18]|(1|8|36*4)(3|56*4)*(0|7|56*[18]))|(4|[07]6*3|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(5|[07]6*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(3|63*[07]|(1|8|63*5)(6|43*5)*(1|8|43*[07])|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(5|36*[18]|(1|8|36*4)(3|56*4)*(0|7|56*[18])))|(6|53*4|(0|7|53*5)(6|43*5)*(5|43*4)|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))|(4|[07]6*3|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(5|[07]6*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(0|7|63*4|(1|8|63*5)(6|43*5)*(5|43*4)|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))))(1|8|(0|7|[29]6*4)(3|56*4)*(4|56*5)|[29]6*5|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))|(6|(0|7|[29]6*4)(3|56*4)*(2|9|56*3)|[29]6*3|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3)))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(0|7|63*4|(1|8|63*5)(6|43*5)*(5|43*4)|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))))*(4|34*5|(0|7|34*[18]|(2|9|34*3)(6|[07]4*3)*(4|[07]4*[18]))(3|56*4|(6|56*[07])(4|36*[07])*(1|8|36*4))*(0|7|64*5|(5|64*3)(6|[07]4*3)*(1|8|[07]4*5))|(2|9|34*3)(6|[07]4*3)*(1|8|[07]4*5)|(6|(0|7|[29]6*4)(3|56*4)*(2|9|56*3)|[29]6*3|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3)))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(3|63*[07]|(1|8|63*5)(6|43*5)*(1|8|43*[07])|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(5|36*[18]|(1|8|36*4)(3|56*4)*(0|7|56*[18])))))*(3|53*[18]|(0|7|53*5)(6|43*5)*(2|9|43*[18])|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(6|36*[29]|(1|8|36*4)(3|56*4)*(1|8|56*[29]))|(4|[07]6*3|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(5|[07]6*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(4|63*[18]|(1|8|63*5)(6|43*5)*(2|9|43*[18])|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(6|36*[29]|(1|8|36*4)(3|56*4)*(1|8|56*[29])))|(6|53*4|(0|7|53*5)(6|43*5)*(5|43*4)|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))|(4|[07]6*3|(1|8|53*6|(0|7|53*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(5|[07]6*4)(3|56*4)*(2|9|56*3))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(0|7|63*4|(1|8|63*5)(6|43*5)*(5|43*4)|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))))(1|8|(0|7|[29]6*4)(3|56*4)*(4|56*5)|[29]6*5|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))|(6|(0|7|[29]6*4)(3|56*4)*(2|9|56*3)|[29]6*3|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3)))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(0|7|63*4|(1|8|63*5)(6|43*5)*(5|43*4)|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(2|9|36*5|(1|8|36*4)(3|56*4)*(4|56*5))))*(5|34*6|(0|7|34*[18]|(2|9|34*3)(6|[07]4*3)*(4|[07]4*[18]))(3|56*4|(6|56*[07])(4|36*[07])*(1|8|36*4))*(1|8|64*6|(5|64*3)(6|[07]4*3)*(2|9|[07]4*6))|(2|9|34*3)(6|[07]4*3)*(2|9|[07]4*6)|(6|(0|7|[29]6*4)(3|56*4)*(2|9|56*3)|[29]6*3|(3|[07]3*6|(2|9|[07]3*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3)))(5|[18]6*3|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(0|7|36*3|(1|8|36*4)(3|56*4)*(2|9|56*3))|(6|[18]6*4)(3|56*4)*(2|9|56*3))*(4|63*[18]|(1|8|63*5)(6|43*5)*(2|9|43*[18])|(2|9|63*6|(1|8|63*5)(6|43*5)*(0|7|43*6))(4|36*[07]|(1|8|36*4)(3|56*4)*(6|56*[07]))*(6|36*[29]|(1|8|36*4)(3|56*4)*(1|8|56*[29]))))))+


    10795 characters, leading zeros forbidden



    0|((foo)0*)+, where the above regex is (0|foo)+.



    Explanation



    Numbers divisible by 7 are matched by the obvious finite automaton with 7 states Q = {0, …, 6}, initial and final state 0, and transitions d: i ↦ (10i + d) mod 7. I converted this finite automaton into a regular expression, using recursion on the set of allowed intermediate states:



    Given i, j ∈ Q and S ⊆ Q, let f(i, S, j) be a regular expression that matches all automaton paths from i to j using only intermediate states within S. Then,



    f(i, ∅, j) = (j − 10i) mod 7,



    f(i, S ∪ {k}, j) = f(i, S, j) ∣ f(i, S, k) f(k, S, k)* f(k, S, j).



    I used dynamic programming to choose k so as to minimize the length of the resulting expression.


    I think you have to add 2 character for in the leading zero case, since I guess zero has to be allowed `0|((foo)0*)+`

    I have commented on the question, but by common sense, "no leading zero" usually means that no redundant leading 0, but it does not exclude the number zero.

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Content dated before 7/24/2021 11:53 AM