Store the registers as keys in a hash of hashes, use the values as the inner keys. After the file has been processed, iterate over the registers and count how many keys the inner hashes have. Those with a single key are the constant registers.

#!/usr/bin/perl
use warnings;
use strict;
use feature qw{ say };

my %R;
while (<<>>) {
    chomp;
    my ($register, $value) = split /,\s*/;
    ++$R{$register}{$value}
}
for my $register (keys %R) {
    say $register, "\t",
        keys %{ $R{$register} } > 1 ? 'variable' : 'constant';
}
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