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**Assigned:** Fri 02-11-11

**Due:** Fri 02-18-11

- 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.

When a problem asks for a context-free grammar, you *must* describe what each variable in
your context-free grammar does, in a manner similar to the
solution given in
the handout.

When you are asked to construct a PDA for a given language. You should give finite state diagrams for such PDAs, similar to those given in class and in Figures 2.15, 2.17, and 2.19 from the Sipser text.

To demonstrate that a given grammar is ambiguous, you must show multiple left-most (or right-most) derivations for a string in the given language. (See pp. 105-106 of the Sipser text.) To attach a "meaning" to any such derivation, you will likely need to consider the parse trees associated with these derivations.

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

**Points:** 20 pts per problem

- Exercise 2.4 (b,c)

- Exercise 2.6 (d)

- Exercise 2.4 (e)
- Construct a CFG for the following language:
{

*a*|^{i }b^{j}*i*<=*j*<= 2*i*}

- Exercises 2.9 and 2.10.

- Give finite state diagrams for PDAs which accept the languages
described in Exercises 2.4 (d) and 2.6 (c).
*Hint:*Make judicious use of non-determinism. - Problem 2.27 (a).
*Hint:*The ambiguity present in the grammar shown in Exercise 2.27 is due to the`if-then`

and`if-then-else`

statements. The ambiguity you will discover is referred to as the "dangling else" ambiguity.

Harriet Fell

College of Computer Science, Northeastern University

360 Huntington Avenue #202WVH

Boston, MA 02115

Phone: (617) 373-2198 / Fax: (617) 373-5121

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The URL for this document is: http://www.ccs.neu.edu/home/fell/CS3800/Homeworks/hw.05.html