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**Assigned:** Fri 01-28-11

**Due:** Fri 02-04-11

- Please review the grading policy outlined in the course information page.
- 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 followingProblem 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.

- 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.

**Required:** 5 of the following 6 problems

**Points:** 20 pts per problem

- 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*.

- Construct a DFA which accepts the following language over the alphabet {0,1}:
- Exercise 1.21
- Convert the following finite automata to regular expressions:
- machine M
_{1}from Figure 1.4 and - machine M
_{1}from Exercise 1.1.

- machine M
- Problem 1.31
- Problem 1.34. (You may assume the result claimed in Problem 1.31.)
- Problem 1.38

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