jettero has asked for the wisdom of the Perl Monks concerning the following question:

I was just messing around with Quantum::Superpositions, which I've read through a few times now. I can't think of anything useful to do with it, so I've been trying to trick it into solving sudoku puzzles. I can't figure out how to chain logic statements though. It was simple enough to build my sudoku memory structure and start comparing rows, cols and cells in a purely looping iterative way, but this isn't really about that. I'm on a simpler step that follows. 
use strict;
use Quantum::Superpositions;

my $s = any( 1 .. 4 );
   $s = $s != 1;
   $s = $s != 2;
my @e = eigenstates( $s );

print "Am I on to something? @e\n";

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The eigen states are (helpfully) 3 and 4. Now, suppose I have another superposition that's also any 1 through 4 that isn't equal to $t? Then what? I'd expect ... 

my $t = any(1 .. 4); $t = $t != $s;

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... to give me a super postion of 1 .. 4, but it gives 3 and 4 instead. Sadly, it's also pretty obvious that it doesn't have the capacity to retain all the implications of $t != $s and $s != 1 and $s != 2 — which would make $t 1 through 4 remembering somehow that it's not equal to $s. I tried one more thing before I realized I either didn't know how to approach the problem, or it simply wasn't possible without magic: 
   $t = $t != $_ for eigenstates( $s );

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Unhelpfully, this makes $t the superposition of 1 and 2, which isn't quite what I was going for... But it at least made me realize I didn't have any idea what to do next.

I'd give up and forget the topic completely, but supposedly perl6 will have this sort of stuff (called junctions), so I'd like to learn more about the kinds of problems you can try to (and will never be able to) solve with this stuff.

Is solving sudoku puzzles with QS and/or junctions even remotely possible?

-Paul

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Re: sudoku via superpositions
by pKai (Priest) on Jun 29, 2007 at 09:58 UTC
    ... to give me a super postion of 1 .. 4
    D:\>perl -MQuantum::Superpositions -e "print eigenstates(any(1..4)!=an
+y(2,3))"
32
D:\>perl -MQuantum::Superpositions -e "print eigenstates(any(2,3)!=any
+(1..4))"
4132

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    Seems that processing any()<op>any() is not symmetric. Doing it the other way round, you'll get your desired result.

    No idea though, if its of any use in solving Sudokus.

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      This is really interesting stuff. I played around with they asymmetry of it, but I didn't get any closer. The any(1,2,3,4) result would (it seems to me) have to "know" that it wasn't one of the any(1,2) to be of any value...

      Perhaps I'm just picturing it wrong.

      -Paul

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        If you read it as do any of 1,2,3,4 match any of 1,2; then the answer is Yes 1 matches 1 and 2 matches 2, so the result is (1,2): 

        print eigenstates( any(1,2,3,4) == any(1,2) );;
1 2

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        The confusing one is eigenstates( any(1,2,3,4) != any(1,2) )

        To me that reads as do any of these not match any of those. Stepping through you get

        1. 1 does not match 2, so add 1 to the result.
        2. 2 does not match 1, so add 2 to the result.
        3. 3 does not match 1 so add 3 to the result.
        4. 3 does not match 2 so add 3 to the result.
        5. 4 does not match 1 so add 4 to the result.
        6. 4 does not match 2 so add 4 to the result.

        So the result is (1, 2, 3, 3, 4, 4), but similar states collapse, so (1, 2, 3, 4).

        So all of the first 'set' do not match at least one of the second set. But that's not what you get: 

        print eigenstates( any(1,2,3,4) != any(1,2) );;
1 2

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        Doing it the other way around, you get: 

        print eigenstates( any(1,2) != any(1,2,3,4) );;
4 1 3 2

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        Which also doesn't make sense because 3 & 4 are not even a part of the first set. (And I don't think the order is defined, so that's not a clue.)

        Which tends to imply that the result of any(set1) != any(set2) means anything from set 2 that can not match something in set one, which is all of set2. And that just seems wrong to me.

        There's probably some deeply meaningful reason for that, but it is certainly unintuative. At which point I gave up trying to understand.

        Examine what is said, not who speaks -- Silence betokens consent -- Love the truth but pardon error.
        "Science is about questioning the status quo. Questioning authority".
        In the absence of evidence, opinion is indistinguishable from prejudice.
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Re: sudoku via superpositions
by Brovnik (Hermit) on Feb 26, 2008 at 20:14 UTC
    I submitted the first Sudoku solver on Perlmonks a while back which used Superpositions. SuDoKu solver

    --
    Brovnik
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