You can't use strings to index arrays. But you could use a 2D hash instead.

The problem is, a 8000x8000 array is going to consume close to 2GB of ram, and a 2D hash of the same dimensions considerably more.

However, since you are only doing a boolean test, there is no need to actually store any values in the hash. Hashes have a very nice exists test.

So, instead of storing 0 or 1 for each pair, you could make a sparse 2D hash by only creating keys (but assigning no value!) for those that are true. Then your test simple becomes if( exists $hash{ $first }{ $second } ){ ... which if the ratio of true to false is less than ~50%, will save you memory relative to an array(~1.7GB .v. ~2GB)

But, for best speed and minimal memory consumption, whenever I see "0 or 1" I think bit vectors. An array of 8000 bitstrings, each with 8000 bits (1000 bytes) requires just 8MB:

@vecs = ('')x8000; 
for my $_1 ( 0 .. 7999 ) { 
    vec( $vecs[ $_1 ], $_, 1 ) = (rand() > 0.5 ) for 0 .. 7999 
};;

print total_size \@vecs;;
8494224
[download]

And lookups are very fast:

$t = time; 
for my $_1 ( 0 .. 7999 ) {  
    vec( $vecs[ $_1 ], $_, 1 ) ? ++$true : ++$false for 0 .. 7999 
}; 
print "$true $false", time() - $t;;
31998302 32001698 15.6879999637604
[download]

At 4 milllion lookups/second, it beats hashes and probably arrays too. Definitely, if their size pushes you into swapping.