CMPSCI 601: Theory of Computation

David Mix Barrington

Spring, 2003

Homework Assignment #4

Due Friday 26 March 2004 2:00 p.m. EST to CMPSCI office drop box

(fax by Wed 7 April 2:00 p.m. EST for off-campus students)

• Question 1 (15): Prove that there exists a total recursive function that is not primitive recursive. (Hint: Define your function and then prove by induction on either p.r. definitions or Bloop programs that the function they compute is not your function. Look up Ackermann's function in a book or on the web.)

• Question 2 (15): Prove that a function f from N^k to N is general recursive (as defined in Lecture 11) iff it is computable in Floop (as defined in Lecture 11).

• Question 3 (10): Describe a poly-time algorithm for the language EmptyCFL defined in Lecture 12.

• Question 4 (60): Do the following problems in [BE], most but not all of which are to be submitted electronically: 9.5, 9.12, 9.16, 10.9, 11.20, 11.38, 12.21, 13.13, 13.29, 18.11, 18.12, 18.16 (five points each).

Last modified 12 March 2003