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<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Guest Speaker<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Presented by: <st1:City w:st="on">Toyota</st1:City>
Technological Institute at <st1:City w:st="on"><st1:place w:st="on">Chicago</st1:place></st1:City><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Speaker: Andrej Bogdanov<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Speaker’s home page: <a
href="http://dimacs.rutgers.edu/~adib/">http://dimacs.rutgers.edu/~adib/</a><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Date: Friday, May 4, 2007<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Time: 10:00<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Location: TTI-C Conference room<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Title: Average-case hardness for NP<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>Abstract:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>The gold standard of difficulty for a computational problem
is NP hardness.<span style='mso-spacerun:yes'> </span>However, NP hard
instances of problems are quite atypical.<span style='mso-spacerun:yes'>
</span>In practice, and in many theoretical settings as well,<o:p></o:p></span></font></p>
<p class=MsoNormal><span class=GramE><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial'>one</span></font></span><font
size=2 face=Arial><span style='font-size:10.0pt;font-family:Arial'> sometimes
adopts the view that NP hard instances are so rare that they present no serious
obstacle to the design of efficient algorithms Yet experience tells us that
some NP problems are intractable even on typical instances.<span
style='mso-spacerun:yes'> </span>This assumption is a fundamental axiom
of modern cryptography.<span style='mso-spacerun:yes'> </span>So <span
class=GramE>far</span> computer science has been unable to explain why this
happens.<span style='mso-spacerun:yes'> </span>In this talk, I will focus
on two basic questions:<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>* What is a typical instance?<span
style='mso-spacerun:yes'> </span>* Can the extensive theory of NP
hardness be used to explain why for certain problems typical instances are also
hard?<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>These two questions will give a glimpse of the central role
that average-case complexity plays in the theory of computation.<o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><span class=GramE><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial'>If you have any questions or would
like to meet the speaker,</span></font></span><font size=2 face=Arial><span
style='font-size:10.0pt;font-family:Arial'> please contact Ponda Barnes at <a
href="mailto:pondabarnes@tti-c.org">pondabarnes@tti-c.org</a><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'>For future TTI-C talks and events please got to <a
href="http://ttic.uchicago.edu/cal/month.php">http://ttic.uchicago.edu/cal/month.php</a><o:p></o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
<p class=MsoNormal><font size=2 face=Arial><span style='font-size:10.0pt;
font-family:Arial'><o:p> </o:p></span></font></p>
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