Here is an algorithm - certainly not the best - that would work:
If you could load your dictionary into memory:
my @words = <DICTIONARY>;
Then it is a simple process of taking your input letters, say
art and doing:
#! /usr/bin/perl -w
use strict;
my $input = 'art';
# Read words from a file instead.
my @words = ('tar', 'rat', 'fake', 'at', 'unknown');
my $regex = qr{[$input]+};
my @matches = grep /^$regex$/, @words;
print "$_\n" for @matches;
Beware of: upper/lower case in input and in the dictionary, the massive amount of memory the words array will consume...
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