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<p class="MsoNormal"><span style="color:#1F497D">| </span>It seems like it should be possible. If we restrict the problem so that multiple simultaneous intermediate results are not allowed, then this certainly seems like a group-theory question. Do you know
anyone who is a computational group theory expert?<o:p></o:p></p>
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<p class="MsoNormal"><span style="color:#1F497D">| </span>Since shuffles that repeat indices are permitted (e.g. [0,1,2,3] -> [1,1,2,3]), some shuffles don't have inverses, so it's unlikely that the problem will be very amenable to group theoretic inquiry (unless
there is some clever way to represent the operations<span style="color:#1F497D"><o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">|
</span>that isn't simply how they rearrange the inputs). Also the fact that e.g. the AVX instruction PSHUFB can put 0's into the result without being in the source seems like a difficult obstacle to formalize group theoretically.<span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p></o:p></span></p>
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<p class="MsoNormal"><span style="color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Note that there's a specialisation of groups referred to as monoids (http://en.wikipedia.org/wiki/Monoid ) which essentially deal with transformations which
are non-invertible. So there is a branch of algebra that studies such things. However, I'm not in any way expert on monoids and their algorithms. (To the extent I've thought about variants of groups in compiler design, I've been interested in how groupoids
might be able to represent some things.)<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Cheers,<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D">Dave<o:p></o:p></span></p>
<p class="MsoNormal"><span style="font-size:11.0pt;font-family:"Calibri","sans-serif";color:#1F497D"><o:p> </o:p></span></p>
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