CSU390 08SP: Homework 03

Assigned: Thu 31 Jan 2008
Due: Thu 07 Feb 2008

General Instructions

1. Please review the grading policy outlined in the course information page.

2. On the first page of each part of your solution write-up, you must make explicit which problems are to be graded for "regular credit", which problems are to be graded for "extra credit", and which problems you did not attempt. Please use a table something like the following

   Problem	01	02	03	04	05	06	07	08	09	...
   Credit	RC	RC	RC	EC	RC	RC	NA	RC	RC	...

   where "RC" is "regular credit", "EC" is "extra credit", and "NA" is "not applicable" (not attempted). Failure to do so will result in an arbitrary set of problems being graded for regular credit, no problems being graded for extra credit, and a five percent penalty assessment.

3. You must also write down with whom you worked on the assignment. If this changes from problem to problem, then you should write down this information separately with each problem.

Problems

Required: 5 of the following 7 problems
Points: 20 pts per problem

1. A string x is said to be a subsequence of a string y if the symbols in x appear, in order, within y. For example, the string x = aab is a subsequence of the string y = babab since the symbols a, a, and b appear in order within y; i.e.,

   

   However, the string aab is not a subsequence of babb.

   • Construct a DFA which accepts the following language over the alphabet {0,1}:

     L = {w : 110 is a subsequence of w}.

   • Devise a regular expression for L.

2. Exercise 1.21

3. Convert the following finite automata to regular expressions:
   • machine M₁ from Figure 1.4 and
   • machine M₁ from Exercise 1.1.

4. Problem 1.31

5. Problem 1.34. (You may assume the result claimed in Problem 1.31.)

6. Problem 1.38

7. Problem 1.40, part (b)

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