CSG714 04S: Homework 05

Assigned: Wed 11 Feb 2004
Due: Wed 18 Feb 2004 (This assignment cannot be accepted late!)

Note: This assignment cannot be accepted beyond its due date as I will distribute solutions at that time in preparation for the midterm exam.

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 6 problems
Points: 20 pts per problem

1. Problem 3.9

2. 1. Problem 3.14

      Hint: The use of multi-tape TMs and non-determinism may simplify your solutions.

   2. Prove that the decidable and recognizable languages are closed under FirstHalf. (See HW01, Problem 9, for the definition of FirstHalf.)

3. Problem 4.15 and 4.19

4. Problem 4.17

   Hint: For half of your proof, let y be an appropriate sequence of configurations.

5. Problem 5.10

   Note: The material from Chapter 5 is not necessary to solve this problem.

6. Problem 5.15

   Note: The material from Chapter 5 is not necessary to solve this problem.

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