http:^^www.cs.washington.edu^education^courses^322^96w^hw9^hw9.html

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Date: Wed, 08 Jan 1997 20:37:25 GMTServer: NCSA/1.4.2Content-type: text/html<!DOCTYPE HTML PUBLIC "-//W3O//DTD W3 HTML 2.0//EN"><!Converted with LaTeX2HTML 95 (Thu Jan 19 1995) by Nikos Drakos (nikos@cbl.leeds.ac.uk), CBLU, University of Leeds ><HEAD><TITLE>CSE 322 Assignment 9 Due Friday, March 1, 1996</TITLE></HEAD><BODY><meta name="description" value="CSE 322 Assignment 9 Due Friday, March 1, 1996"><meta name="keywords" value="hw9"><meta name="resource-type" value="document"><meta name="distribution" value="global"><P> <BR> <HR><A NAME=tex2html1 HREF="node1.html"><IMG ALIGN=BOTTOM ALT="next" SRC="http://www.cs.washington.edu/general/latex2html_icons//next_motif.gif"></A>   <IMG ALIGN=BOTTOM ALT="up" SRC="http://www.cs.washington.edu/general/latex2html_icons//up_motif_gr.gif">   <IMG ALIGN=BOTTOM ALT="previous" SRC="http://www.cs.washington.edu/general/latex2html_icons//previous_motif_gr.gif">         <BR><B> Next:</B> <A NAME=tex2html2 HREF="node1.html">   About this document </A><BR> <HR> <P><P><H1>CSE 322 Assignment 9 Due Friday, March 1, 1996</H1><P><STRONG></STRONG><P><P><STRONG></STRONG><P><P><OL><LI>Let <IMG  ALIGN=MIDDLE ALT="" SRC="img1.gif"> and<IMG  ALIGN=MIDDLE ALT="" SRC="img2.gif"> be NFAs.Construct a new NFA <b>M</b> that accepts the language<P><IMG  ALIGN=BOTTOM ALT="" SRC="img3.gif"><P>Think of <b>L</b> as the set of arbitrary shuffles of strings from <IMG  ALIGN=MIDDLE ALT="" SRC="img4.gif"> and<IMG  ALIGN=MIDDLE ALT="" SRC="img5.gif">.  For example, if <b>aab</b> is in <IMG  ALIGN=MIDDLE ALT="" SRC="img6.gif"> and <b>bb</b> is in <IMG  ALIGN=MIDDLE ALT="" SRC="img7.gif"> thenthe strings <b>aabbb, ababb, bbaab</b> and many other strings are in <b>L</b>.Hint: The machine will have to run both <IMG  ALIGN=MIDDLE ALT="" SRC="img8.gif"> and <IMG  ALIGN=MIDDLE ALT="" SRC="img9.gif"> in parallel, butonly one at a time.  Thus, a cross product-like construction is in order.<P>You don't have to prove that your construction is correct, but you muststate a behavioral lemma which could be used in such a proof.<P><LI>Show that the set of all strings over the alphabet <IMG  ALIGN=MIDDLE ALT="" SRC="img10.gif"> with anequal number of <b>a</b>'s as <b>b</b>'s is not a regular set.  You may use closureproperties of regular languages and the fact that the language<IMG  ALIGN=MIDDLE ALT="" SRC="img11.gif"> is not regular.<P><LI>Show that the language <IMG  ALIGN=MIDDLE ALT="" SRC="img12.gif"> is not regular.  You will have prove this by contradiction from first principles.</OL><BR> <HR><UL> <LI> <A NAME=tex2html3 HREF="node1.html#SECTION00010000000000000000">   About this document ... </A></UL><BR> <HR><P><ADDRESS><I>James Fix <BR>Tue Feb 27 08:16:35 PST 1996</I></ADDRESS></BODY>

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