# 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