CSU390 03F: Homework 07

Assigned: Wed 19 Nov 2003
Due: Wed 26 Nov 2003 (no later than 5pm)

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: 3 of the following 4 problems
Points: 25 pts per problem

1. Exercise 5.12

2. Prove that the following language is undecidable.
   L = {<M> | M is a Turing machine and |L(M)| >= 2}

3. Prove that the following language is undecidable.
   L = {<M> | M is a Turing machine, and M is a decider}

4. Prove that the following language is undecidable.
   L = {<M₁,M₂,k> | M₁ and M₂ are Turing machines, and |L(M₁) int L(M₂)| >= k}

   Here "int" is set intersection.

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