**Assigned:** Wed 10-13

**Due:** Wed 10-20

- 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

- Construct both a CFG and a PDA for the following language:
{a
^{i}b^{k}| i <= k <= 2i}.
Prove that your CFG is correct.
Prove that your PDA is correct.
- Consider the following language:
{a
^{k}b^{2k}| 0 <= k }. Give two CFG grammars for L, one that is ambiguous and one that is not. Note: you have to prove that one grammar is ambiguous and that the other one is not. - Problem 2.19.
- Problem 2.30 parts a, d.
- Problem 2.31.
- Problem 2.32.

viola@ccs.neu.edu