<?xml version='1.0' encoding='UTF-8'?><?xml-stylesheet href="http://www.blogger.com/styles/atom.css" type="text/css"?><feed xmlns='http://www.w3.org/2005/Atom' xmlns:openSearch='http://a9.com/-/spec/opensearchrss/1.0/' xmlns:georss='http://www.georss.org/georss' xmlns:gd='http://schemas.google.com/g/2005' xmlns:thr='http://purl.org/syndication/thread/1.0'><id>tag:blogger.com,1999:blog-2104131774245696298</id><updated>2012-02-29T10:41:12.736-08:00</updated><category term='Example Solution'/><category term='Homework 1'/><title type='text'>FLAC What's New</title><subtitle type='html'>&lt;a href="http://www.cs.cmu.edu/~lblum/flac/index.htm"&gt;FLAC Spring 2012&lt;/a&gt; &lt;br&gt;


&lt;a href="http://www.cs.cmu.edu/~lblum/flac/schedule.html"&gt;Schedule&lt;/a&gt; &lt;br&gt;

&lt;a href="http://www.cs.cmu.edu/~lblum/flac/project.html"&gt;Project Page&lt;/a&gt;</subtitle><link rel='http://schemas.google.com/g/2005#feed' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/posts/default'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default?max-results=100'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/'/><link rel='hub' href='http://pubsubhubbub.appspot.com/'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><generator version='7.00' uri='http://www.blogger.com'>Blogger</generator><openSearch:totalResults>12</openSearch:totalResults><openSearch:startIndex>1</openSearch:startIndex><openSearch:itemsPerPage>100</openSearch:itemsPerPage><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-7706467677426142015</id><published>2012-02-29T10:40:00.000-08:00</published><updated>2012-02-29T10:41:12.749-08:00</updated><title type='text'>Homework 5 Solutions Posted</title><content type='html'>&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-7706467677426142015?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/7706467677426142015/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-5-solutions-posted.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7706467677426142015'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7706467677426142015'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-5-solutions-posted.html' title='Homework 5 Solutions Posted'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-7715056374946858423</id><published>2012-02-29T10:19:00.002-08:00</published><updated>2012-02-29T10:22:37.707-08:00</updated><title type='text'>Homework 6, Problem 4 Clarification</title><content type='html'>In problem 4 you should assume that the input of a Turing Machine M is always a binary string (the input alphabet is {0,1}).&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-7715056374946858423?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/7715056374946858423/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-6-problem-4-clarification.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7715056374946858423'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7715056374946858423'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-6-problem-4-clarification.html' title='Homework 6, Problem 4 Clarification'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-5472654393997813432</id><published>2012-02-27T14:08:00.003-08:00</published><updated>2012-02-27T14:19:18.464-08:00</updated><title type='text'>Homework 5 Typo</title><content type='html'>There was a small typo in problem 1(B=&amp;gt;t_kBa_k should have been B=&amp;gt;b_kBa_k). The problem has been corrected on the web site.&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-5472654393997813432?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/5472654393997813432/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-5-typo.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/5472654393997813432'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/5472654393997813432'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-5-typo.html' title='Homework 5 Typo'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-4413489947871178188</id><published>2012-02-25T15:32:00.001-08:00</published><updated>2012-02-25T15:32:37.121-08:00</updated><title type='text'>Homework 4 (Solutions Correction)</title><content type='html'>There was an error in the Turing machine diagram for the Problem 1 solution. &amp;nbsp;The figure has been corrected, and an updated PDF of the solutions was uploaded this afternoon. &amp;nbsp;Sorry for the confusion!&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-4413489947871178188?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/4413489947871178188/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-4-solutions-correction.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/4413489947871178188'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/4413489947871178188'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-4-solutions-correction.html' title='Homework 4 (Solutions Correction)'/><author><name>Greg H.</name><uri>http://www.blogger.com/profile/16998934265404718097</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-7341832546258941030</id><published>2012-02-22T20:42:00.000-08:00</published><updated>2012-02-22T20:49:52.901-08:00</updated><title type='text'>Project Advisors</title><content type='html'>&lt;!--[if gte mso 9]&gt;&lt;xml&gt; 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  &lt;w:lsdexception locked="false" priority="32" semihidden="false" unhidewhenused="false" qformat="true" name="Intense Reference"&gt;   &lt;w:lsdexception locked="false" priority="33" semihidden="false" unhidewhenused="false" qformat="true" name="Book Title"&gt;   &lt;w:lsdexception locked="false" priority="37" name="Bibliography"&gt;   &lt;w:lsdexception locked="false" priority="39" qformat="true" name="TOC Heading"&gt;  &lt;/w:LatentStyles&gt; &lt;/xml&gt;&lt;![endif][if gte mso 10]&gt; &lt;style&gt;  /* Style Definitions */  table.MsoNormalTable  {mso-style-name:"Table Normal";  mso-tstyle-rowband-size:0;  mso-tstyle-colband-size:0;  mso-style-noshow:yes;  mso-style-priority:99;  mso-style-qformat:yes;  mso-style-parent:"";  mso-padding-alt:0in 5.4pt 0in 5.4pt;  mso-para-margin:0in;  mso-para-margin-bottom:.0001pt;  mso-pagination:widow-orphan;  font-size:11.0pt;  font-family:"Calibri","sans-serif";  mso-ascii-font-family:Calibri;  mso-ascii-theme-font:minor-latin;  mso-fareast-font-family:"Times New Roman";  mso-fareast-theme-font:minor-fareast;  mso-hansi-font-family:Calibri;  mso-hansi-theme-font:minor-latin;  mso-bidi-font-family:"Times New Roman";  mso-bidi-theme-font:minor-bidi;} &lt;/style&gt; &lt;![endif]--&gt;&lt;b&gt;&lt;span style="font-size:12.0pt;font-family:&amp;quot;Times&amp;quot;,&amp;quot;serif&amp;quot;; mso-fareast-font-family:&amp;quot;Times New Roman&amp;quot;;color:black;mso-ansi-language:EN-US; mso-fareast-language:EN-US;mso-bidi-language:AR-SA"&gt;Greg&lt;/span&gt;&lt;/b&gt;&lt;span style="font-size:12.0pt;font-family:&amp;quot;Times&amp;quot;,&amp;quot;serif&amp;quot;;mso-fareast-font-family: &amp;quot;Times New Roman&amp;quot;;color:black;mso-ansi-language:EN-US;mso-fareast-language: EN-US;mso-bidi-language:AR-SA"&gt;&lt;br /&gt;Chase Brownell&lt;br /&gt;Will Devanny&lt;br /&gt;Wade Gordon&lt;br /&gt;Max Illfelder&lt;br /&gt;Joseph Lee&lt;br /&gt;Kellie Medlin&lt;br /&gt;Laura Scharff&lt;br /&gt;&lt;br /&gt;&lt;b&gt;Jeremiah&lt;/b&gt;&lt;br /&gt;Igor Balla&lt;br /&gt;Rick Benua&lt;br /&gt;Eric Cheek&lt;br /&gt;Alex Crichton&lt;br /&gt;Robert Liu&lt;br /&gt;Paul Schultz&lt;br /&gt;Max Tucker&lt;br /&gt;&lt;br /&gt;&lt;b&gt;Lenore&lt;/b&gt;&lt;br /&gt;Ved Basu&lt;br /&gt;Andrew Israel&lt;br /&gt;Jason MacDonald&lt;br /&gt;William Macrae&lt;br /&gt;Mohith Muddasani&lt;br /&gt;Sanjeev Reddy&lt;br /&gt;Divya Sharma&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-7341832546258941030?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/7341832546258941030/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/project-advisors.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7341832546258941030'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7341832546258941030'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/project-advisors.html' title='Project Advisors'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-4287514671066865119</id><published>2012-02-02T11:39:00.000-08:00</published><updated>2012-02-02T11:49:25.120-08:00</updated><title type='text'>Homework 3 (Revised Hint)</title><content type='html'>We had originally intended for the state "101" in problem 1(b) to be an accept state. For problem 1(b) you may either&lt;br /&gt;  (1) minimize the original DFA (presented in the homework).&lt;br /&gt;  (2) minimize the new DFA (after changing "101" to an accept state).&lt;br /&gt;&lt;br /&gt;You will be given full credit for either answer. We will assume that you are minimizing the original DFA (option 1) unless clearly indicated.&lt;br /&gt;&lt;br /&gt;Note: If you have not solved the problem yet (or even if you have) we would recommend minimizing the new DFA. The hint for homework 3 problem 2 will make more sense if you make "101" an accept state.&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-4287514671066865119?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/4287514671066865119/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-3-revised-hint.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/4287514671066865119'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/4287514671066865119'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/02/homework-3-revised-hint.html' title='Homework 3 (Revised Hint)'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-9021186981222684932</id><published>2012-01-26T10:35:00.000-08:00</published><updated>2012-01-26T10:40:23.145-08:00</updated><title type='text'>Monday Office Hours Moved to NSH 1505</title><content type='html'>The super office hours (Monday 3:30-5:30 PM) have been relocated to NSH 1505 for the rest of the semester. Formerly, the problem solving session was held in GHC 2109.&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-9021186981222684932?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/9021186981222684932/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/monday-office-hours-moved-to-nsh-1505.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/9021186981222684932'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/9021186981222684932'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/monday-office-hours-moved-to-nsh-1505.html' title='Monday Office Hours Moved to NSH 1505'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-3304179383647059477</id><published>2012-01-18T22:07:00.001-08:00</published><updated>2012-01-18T22:07:36.338-08:00</updated><title type='text'>Homework 1</title><content type='html'>&lt;!--[if gte mso 9]&gt;&lt;xml&gt; 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  &lt;w:lsdexception locked="false" priority="32" semihidden="false" unhidewhenused="false" qformat="true" name="Intense Reference"&gt;   &lt;w:lsdexception locked="false" priority="33" semihidden="false" unhidewhenused="false" qformat="true" name="Book Title"&gt;   &lt;w:lsdexception locked="false" priority="37" name="Bibliography"&gt;   &lt;w:lsdexception locked="false" priority="39" qformat="true" name="TOC Heading"&gt;  &lt;/w:LatentStyles&gt; &lt;/xml&gt;&lt;![endif]--&gt;&lt;!--[if gte mso 10]&gt; &lt;style&gt;  /* Style Definitions */  table.MsoNormalTable  {mso-style-name:"Table Normal";  mso-tstyle-rowband-size:0;  mso-tstyle-colband-size:0;  mso-style-noshow:yes;  mso-style-priority:99;  mso-style-qformat:yes;  mso-style-parent:"";  mso-padding-alt:0in 5.4pt 0in 5.4pt;  mso-para-margin:0in;  mso-para-margin-bottom:.0001pt;  mso-pagination:widow-orphan;  font-size:11.0pt;  font-family:"Calibri","sans-serif";  mso-ascii-font-family:Calibri;  mso-ascii-theme-font:minor-latin;  mso-fareast-font-family:"Times New Roman";  mso-fareast-theme-font:minor-fareast;  mso-hansi-font-family:Calibri;  mso-hansi-theme-font:minor-latin;  mso-bidi-font-family:"Times New Roman";  mso-bidi-theme-font:minor-bidi;} &lt;/style&gt; &lt;![endif]--&gt;&lt;span style="font-size:12.0pt;font-family:&amp;quot;Times New Roman&amp;quot;,&amp;quot;serif&amp;quot;; mso-fareast-font-family:Calibri;mso-fareast-theme-font:minor-latin;mso-ansi-language: EN-US;mso-fareast-language:EN-US;mso-bidi-language:AR-SA"&gt;There are two minor errors in Homework 1.  In Problem 1(b), "0", "1", and "2" should be called "digits", not letters.  In the definition of min(A) in Problem 2, both instances of "L" should be "A" instead.  The homework PDF was modified to reflect these corrections as of 11:30 p.m. on Wednesday, Jan. 18.&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-3304179383647059477?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/3304179383647059477/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/homework-1.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/3304179383647059477'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/3304179383647059477'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/homework-1.html' title='Homework 1'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-9127250308606086962</id><published>2012-01-18T08:37:00.000-08:00</published><updated>2012-01-18T08:38:20.550-08:00</updated><title type='text'>Fun Applications of the Pigeonhole Principle</title><content type='html'>&lt;!--[if gte mso 9]&gt;&lt;xml&gt; 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 mso-bidi-font-family:"Times New Roman";  mso-bidi-theme-font:minor-bidi;} &lt;/style&gt; &lt;![endif]--&gt;  &lt;p class="MsoPlainText"&gt;&lt;a href="http://mindyourdecisions.com/blog/2008/11/25/16-fun-applications-of-the-pigeonhole-principle/"&gt;http://mindyourdecisions.com/blog/2008/11/25/16-fun-applications-of-the-pigeonhole-principle/&lt;/a&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-9127250308606086962?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/9127250308606086962/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/fun-applications-of-pigeonhole.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/9127250308606086962'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/9127250308606086962'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/fun-applications-of-pigeonhole.html' title='Fun Applications of the Pigeonhole Principle'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-5557297811677300839</id><published>2012-01-17T11:31:00.000-08:00</published><updated>2012-01-17T11:37:33.231-08:00</updated><category scheme='http://www.blogger.com/atom/ns#' term='Homework 1'/><category scheme='http://www.blogger.com/atom/ns#' term='Example Solution'/><title type='text'>Example Homework Solution</title><content type='html'>Here is an example of a well writen homework solution. The answer references problem 1.32 in Sipser (Problem 1.25 in the old edition of Sipser).&lt;br /&gt;&lt;img style="width: 1110px; height: 766px;" 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alt="" /&gt;&lt;br /&gt;Apologies about the formatting. You can right click on the image and select view image.&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-5557297811677300839?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/5557297811677300839/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/example-homework-solution.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/5557297811677300839'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/5557297811677300839'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2012/01/example-homework-solution.html' title='Example Homework Solution'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-3339183284634174645</id><published>2011-12-15T11:20:00.000-08:00</published><updated>2011-12-29T08:30:27.201-08:00</updated><title type='text'>Project Ideas</title><content type='html'>Below are some papers that would be very nice class projects.&lt;span style="font-style: italic;"&gt;&lt;br /&gt;&lt;br /&gt;Smooth Sensitivity and Sampling in Private Data Analysis&lt;/span&gt; by K. Nissim, S. Raskhodnikova and A. Smith (STOC 2007)&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Terminal Backup, 3D Matching, and Covering Cubic Graphs&lt;/span&gt; by E. Anshelevich and A. Karagiozova (STOC 2007).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Resolving the Complexity of Some Data Privacy Problems&lt;/span&gt; by J. Blocki and R. Williams (ICALP 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Simple Deterministic Approximation Algorithms for Counting Matchings&lt;/span&gt; by M. Bayati, D. Gamarnik,D. Katz, C. Nair and P. Tetali (STOC 2007).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Fully Homomorphic Encryption over the Integers&lt;/span&gt; by &lt;span class="citation web"&gt;M.van Dijk, C. Gentry, S. Halevi and V.Vaikuntanathan (IACR 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Regret Minimization and the Price of Total Anarchy &lt;/span&gt;by Avrim Blum, MohammadTaghi Hajiaghayi, Katrina Ligett and  Aaron Roth (STOC 2008).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;A Learning Theory Approach to Non-Interactive Database Privacy &lt;/span&gt;by&lt;span style="font-style: italic;"&gt; &lt;/span&gt;Avrim Blum, Katrina Ligett and Aaron Roth&lt;span style="font-style: italic;"&gt; &lt;/span&gt;(STOC 2008).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Evolvability from Learning Algorithms &lt;/span&gt;by Vitaly Feldman (STOC 2008).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Delegating Computation: Interactive Proofs for Muggles&lt;/span&gt; by Shafi Goldwasser,&lt;br /&gt;Yael Tauman Kalai and Guy N. Rothblum (STOC 2008).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;A Constructive Proof of the Lavasz Local Lemma &lt;/span&gt;by R. Moser (STOC 2009).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Approximating edit distance in near linear time&lt;/span&gt; by A. Andoni and K. Onak (STOC 2009).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Public-key cryptosystems from the worst-case shortest vector problem: extended abstract &lt;/span&gt;by Chris Peikert (STOC 2009).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Finding, minimizing, and counting weighted subgraphs &lt;/span&gt;by V. Vassilevska and R. Williams (STOC 2009).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Perfect matchings in o(n log n) time in regular bipartite graphs &lt;/span&gt;by Ashish Goel, Michael Kapralov and Sanjeev Khanna (STOC 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Public-key cryptography from different assumptions&lt;/span&gt; by Benny Applebaum, Boaz Barak and Avi Wigderson (STOC 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Improving exhaustive search implies superpolynomial lower bounds&lt;/span&gt; by Ryan Williams (STOC 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Interactive privacy via the median mechanism &lt;/span&gt;by Aaron Roth and Tim Roughgarden (STOC 2010).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;A full derandomization of schöning's k-SAT algorithm&lt;/span&gt; by Robin A. Moser and Dominik Scheder (STOC 2011).&lt;br /&gt;&lt;br /&gt;&lt;span style="font-style: italic;"&gt;Stability Yields a PTAS for k-Median and k-Means Clustering &lt;/span&gt;by Awasthi, P.  Blum, A. and  Sheffet, O (FOCS 2010).&lt;br /&gt;&lt;/span&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-3339183284634174645?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/3339183284634174645/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2011/12/project-ideas.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/3339183284634174645'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/3339183284634174645'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2011/12/project-ideas.html' title='Project Ideas'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry><entry><id>tag:blogger.com,1999:blog-2104131774245696298.post-7086241009215906145</id><published>2011-12-15T08:40:00.000-08:00</published><updated>2011-12-15T11:05:38.324-08:00</updated><title type='text'>Helpful Links</title><content type='html'>&lt;p class="MsoNormal" style="margin-bottom:12.0pt"&gt;&lt;span style="font-family:       Symbol;mso-ascii-font-family:&amp;quot;Times New Roman&amp;quot;"&gt;·&lt;/span&gt;&lt;span style="mso-spacerun:yes"&gt;  &lt;/span&gt;&lt;a href="http://en.wikipedia.org/wiki/Finite_state_machine"&gt;&lt;b&gt;&lt;span style="font-size:10.0pt;font-family:&amp;quot;Verdana&amp;quot;,&amp;quot;sans-serif&amp;quot;;color:black;       text-decoration:none;text-underline:none"&gt;The Wiki for FSM's&lt;/span&gt;&lt;/b&gt;&lt;/a&gt;       with lots of neat links. &lt;/p&gt;       &lt;p class="MsoNormal" style="margin-bottom:12.0pt"&gt;&lt;span style="font-family:       Symbol;mso-ascii-font-family:&amp;quot;Times New Roman&amp;quot;"&gt;·&lt;/span&gt;&lt;span style="mso-spacerun:yes"&gt;  &lt;/span&gt;&lt;a href="http://www.cs.cmu.edu/%7Eharchol/gradschooltalk.pdf"&gt;&lt;b&gt;&lt;span style="font-size:10.0pt;font-family:&amp;quot;Verdana&amp;quot;,&amp;quot;sans-serif&amp;quot;;color:black;       text-decoration:none;text-underline:none"&gt;Mor Harchol-Balter's notes&lt;/span&gt;&lt;/b&gt;&lt;/a&gt;       on applying to grad school in computer science. &lt;/p&gt;       &lt;p class="MsoNormal" style="margin-bottom:12.0pt"&gt;&lt;span style="font-family:       Symbol;mso-ascii-font-family:&amp;quot;Times New Roman&amp;quot;"&gt;·&lt;/span&gt;&lt;span style="mso-spacerun:yes"&gt;  &lt;/span&gt;&lt;a href="http://portal.acm.org/toc.cfm?id=SERIES396&amp;amp;idx=SERIES396&amp;amp;type=series&amp;amp;coll=ACM&amp;amp;dl=ACM&amp;amp;part=series&amp;amp;WantType=Proceedings&amp;amp;title=STOC&amp;amp;CFID=36220143&amp;amp;CFTOKEN=50709087"&gt;&lt;b&gt;&lt;span style="font-size:10.0pt;font-family:&amp;quot;Verdana&amp;quot;,&amp;quot;sans-serif&amp;quot;;color:black;       text-decoration:none;text-underline:none"&gt;Electronic version of the       proceedings of STOC&lt;/span&gt;&lt;/b&gt;&lt;/a&gt; &lt;/p&gt;       &lt;p class="MsoNormal" style="margin-bottom:12.0pt"&gt;&lt;span style="font-family:       Symbol;mso-ascii-font-family:&amp;quot;Times New Roman&amp;quot;"&gt;·&lt;/span&gt;&lt;span style="mso-spacerun:yes"&gt;  &lt;/span&gt;&lt;a href="http://ieeexplore.ieee.org/xpl/conhome.jsp?punumber=1000292"&gt;&lt;b&gt;&lt;span style="font-size:10.0pt;font-family:&amp;quot;Verdana&amp;quot;,&amp;quot;sans-serif&amp;quot;;color:black;       text-decoration:none;text-underline:none"&gt;Electronic version of the       proceedings of FOCS&lt;/span&gt;&lt;/b&gt;&lt;/a&gt;. &lt;/p&gt;       &lt;p class="MsoNormal"&gt;&lt;span style="font-family:Symbol;mso-ascii-font-family:       &amp;quot;Times New Roman&amp;quot;"&gt;&lt;/span&gt;&lt;br /&gt;&lt;/p&gt;&lt;div class="blogger-post-footer"&gt;&lt;img width='1' height='1' src='https://blogger.googleusercontent.com/tracker/2104131774245696298-7086241009215906145?l=flac-spring-2012.blogspot.com' alt='' /&gt;&lt;/div&gt;</content><link rel='replies' type='application/atom+xml' href='http://flac-spring-2012.blogspot.com/feeds/7086241009215906145/comments/default' title='Post Comments'/><link rel='replies' type='text/html' href='http://flac-spring-2012.blogspot.com/2011/12/helpful-links.html#comment-form' title='0 Comments'/><link rel='edit' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7086241009215906145'/><link rel='self' type='application/atom+xml' href='http://www.blogger.com/feeds/2104131774245696298/posts/default/7086241009215906145'/><link rel='alternate' type='text/html' href='http://flac-spring-2012.blogspot.com/2011/12/helpful-links.html' title='Helpful Links'/><author><name>jblocki</name><uri>http://www.blogger.com/profile/08267861133300203008</uri><email>noreply@blogger.com</email><gd:image rel='http://schemas.google.com/g/2005#thumbnail' width='16' height='16' src='http://img2.blogblog.com/img/b16-rounded.gif'/></author><thr:total>0</thr:total></entry></feed>
