# CS3800 SP11: Homework 03

Created: Thu 27 Jan 2011

Assigned: Fri 01-28-11
Due: Fri 02-04-11

## Instructions

1. Please review the grading policy outlined in the course information page.
2. On the first page 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 6 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

### Switch to:

Harriet Fell
College of Computer Science, Northeastern University
360 Huntington Avenue #340 WVH,
Boston, MA 02115

Phone: (617) 373-2198 / Fax: (617) 373-5121
The URL for this document is: http://www.ccs.neu.edu/home/fell/CS3800/SP11/hw.03.html