It's not so easy. You can't paste them together, as that might increase the number of mismatches over the threshold.

But you can change the algorithm totally if you want to find the longest matches. Just move the shorter string alongside the longer one, and then for each position try to find the longest match starting there.

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

my $stretch = 10;
my $mismatches = 1;

substr $reference_str, 0, 0, 'x' x (length($small_str) - 1);
$reference_str .= 'x' x (length($small_str) - 1);

for my $start_pos (0 .. length($reference_str) - length($small_str)) {
    my $substr = substr $reference_str, $start_pos, length($small_str)
+;

    my ($from, $diffs) = (0, 0);
    for my $inner_pos (0 .. length($small_str) ) {
        ++$diffs if substr($substr, $inner_pos, 1)
                 ne substr $small_str, $inner_pos, 1;

        if ($diffs > $mismatches || $inner_pos == length($small_str) )
+ {
            say join "\n\t",
                $start_pos + $from + 1 - length $small_str,
                substr($small_str, $from, $inner_pos - $from),
                substr($reference_str, $from + $start_pos, $inner_pos 
+- $from)
                if $inner_pos - $from >= $stretch;

            ++$from until (substr $small_str, $from, 1) ne substr($sub
+str, $from, 1) || $from > $inner_pos;
            ++$from;
            --$diffs;
        }
    }
}
[download]

> was the problem I asked for a question of finding the longest possible match with one mismatch allowed?

Basically, yes.

($q=q:Sq=~/;[c](.)(.)/;chr(-||-|5+lengthSq)`"S|oS2"`map{chr |+ord
}map{substrSq`S_+|`|}3E|-|`7**2-3:)=~y+S|`+$1,++print+eval$q,q,a,
[download]