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<div class="moz-cite-prefix">On 3/13/2017 7:46 AM,
<a class="moz-txt-link-abbreviated" href="mailto:nalini.elkins@insidethestack.com">nalini.elkins@insidethestack.com</a> wrote:<br>
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<blockquote
cite="mid:2119829505.5773849.1489416402134@mail.yahoo.com"
type="cite">
<pre wrap="">It is an interesting problem. For example, we took one 6 character name of a business which is trademarked & ran it through my algorithm, we came up with over 1 million possible permutations. This is because you can use more than one character look-alike.
Lest you think that this doesn't happen, we have already found names registered which use more than one confusable. And, I have only just started my testing.</pre>
</blockquote>
<p><font face="Candara">I keep coming back to the concept of
"perceptual distance".</font></p>
<p><font face="Candara">When you look at individual code points and
call them "confusable" you assert that each such pair has a
perceptual distance that is small enough to fit below a certain
threshold, but that threshold is not zero, nor is the actual
perceptual distance between most code points that are considered
confuable.<br>
</font></p>
<p><font face="Candara">There are two interesting issues with this.</font></p>
<p><font face="Candara">One is that that you may have two pairs of
confusables that have one common member, but the other two
members are far enough apart in perceptual distance to no longer
meet your threshold of confusability.</font></p>
<p><font face="Candara">The other is that code points by themselves
are really not relevant for this, because the real metric should
be the perceptual distance between labels (or even FQDNs).</font></p>
<p><font face="Candara">Just based on labels: if you simultaneously
substitute more than one code point in a label with a potential
confusable, the result may be that the label is now further
apart in perceptual space from the original label than if you
had only substituted one code point at a time. The reason is
that people read words, and having a single code point altered
may not interfere with the process of reading that word, but once
you change two or more, the situation is different.</font></p>
<p><font face="Candara">As a result, I would tentatively conclude
that your claim that those 1 million permutations are all
equally confusable with the original label is likely specious.
It is reasonable to suspect that a good portion of those labels
would look distinctly "odd", if your substitution is based on
ordinary single-code-point confusability thresholds.</font></p>
<p><font face="Candara">That said, there are some labels in certain
scripts for which the variant code points are true equivalents
(whether visual, phonetic or semantic). In those cases, making
multiple substitutions can result in rather large multiplicities
of fully equivalent labels. <br>
</font></p>
<p><font face="Candara">(Note, that if one starts with 0 distance,
or almost 0 distance, in perceptual space, then even multiple
substitutions can be expected to result in negligible perceptual
distance between variant labels --- but that is not usually the
case for the kinds of instances considered under "confusable").</font></p>
<p><font face="Candara">Finally, in considering labels, you'll pick
up the 'rn' vs. 'm' issue: that is, confusables are not 1:1 in
code point space, they may be 1:n or even n:m. (The same is
true for variants that represent true equivalence).</font></p>
<p><font face="Candara">A./</font></p>
<p><font face="Candara">PS: a test whether variants are true
equivalence is whether they satisfy not only symmetry but transitivity.
Anything with a measurable perceptual distance is likely not transitive;
just think of two labels that are (barely) not confusable and
now imagine an "average shape" label. The latter would be confusable
with both, and therefore all three would not obey the
transitivity constraint.<br>
</font></p>
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