# 22C:131 Limits of Computation

1:30-2:20 MWF, Room 205 MLH

Instructor: Sriram V. Pemmaraju
101G MLH, sriram@cs.uiowa.edu, 319-353-2956
Office Hours: 9-10 Tuesday, 11:30-12:30 Wednesday, and 9-10 Friday.

This course is a mathematical exploration of the limits of the power of computers. Some of the questions we ask and attempt to answer are the following. Are there problems that cannot be solved on any computer? How does one determine if a given problem can or cannot be computationally solved? If we place bounds on the resources (time and space) available to a computer, then what say about which problems can and which problems cannot be solved on a computer? How does the power of a computer change, if it has access to random bits? What happens when we relax the notion of solving a problem to "approximately" solving a problem - does this fundamentally change which problems can and which problems cannot be solved on a computer?

In attempting to answer these questions we will study languages, Turing machines, undecidability, the classes of problems P, NP, NP-complete, the Cook-Levin theorem, reductions, randomized algorithms and randomized complexity classes such as BPP, approximation algorithms and hardness of approximation. Time permitting, we will also study interactive proofs.

The TA for this course is Rajiv Raman. Contact information and office hours for Rajiv are:
```		Office: 101K, MLH
Phone: 353-2542
E-mail: rraman@cs.uiowa.edu
URL: www.cs.uiowa.edu/~rraman/
Office hours: Wednesday and Friday, 2:30-3:30
```

## Homeworks and Exams

• Homework 1. Due on Monday, 2/20.
• For Homework 2, solve 5.15, 5.19, 7.18, 7.27, and 7.39. All problem numbers refer to Sipser, 2nd ed. Due on Wednesday, March 8th. Here is a partital mapping between 2nd ed and 1st ed of Sipser, 5.15 -> 5.15, 7.18 -> 7.18, 7.27 -> 7.34, 7.39 -> 7.32. Problem 5.19 is this: In the Silly Post Correspondence Problem, SPCP, in each pair the top string has the same length as the bottom string. Show that SPCP is decidable.
• Solution to midterm exam.
• Homework 3. Due on Wednesday, 4/5. Updated to give mapping from Edition 2 to Edition 1 and one problem is replaced by another. Here are some hints for two of the problems.
• Homework 4. Due on Monday, 5/8.