Here is my attempt:

use strict;
use warnings;
use Data::Dumper;

my @data = 
    map { [ [split /,\s*/, $_->[0]],  [split /,\s*/, $_->[1]] ] }
    map { /\[(.*)\]\s*=>\s*\[(.*)\]/ ? [ $1, $2 ] : () } <DATA>;

my %inverted;
for my $d (@data) {
    undef @{$inverted{$_}}{@{$d->[0]}} for @{$d->[1]};
}

my %invertagain;
push @{ $invertagain{join ",", sort keys %{$inverted{$_}}} }, $_ for k
+eys %inverted;

print Dumper \%invertagain;
__DATA__
[a, b, c] => [1, 2, 3]
[b, c]    => [2, 3, 4, 5]
[a, c, d] => [4, 5, 6, 7]
[d]       => [1, 2, 6]
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