You have the coordinates of the subsequences? Then this should work:
use strict;
use warnings;
use List::Util qw(min);
use Data::Dumper;
my $seq1 = { id => 1,
start => 0,
seq => 'CTGCCACCGCTGT' };
my $seq2 = { id => 1,
start => 5,
seq => 'ACCGCTGTGTTTCGGCCGGCGA'};
print Dumper [ intersection($seq1, $seq2) ];
sub intersection {
# make sure that seq1 is always the first
# subsequence
my ($seq1, $seq2) = sort {$a->{start} <=> $b->{start} }@_;
# determine the start of intersected string ...
my $i_start = $seq2->{start} - $seq1->{start};
# ... and the length
my $i_length = min(length(substr($seq1->{seq},$i_start)),
length($seq2->{seq}));
return ($i_start+1, substr($seq2->{seq}, 0, $i_length));
}