Computational Complexity

Spring 2018

4042 Bren Hall

irani@ics.uci.edu

DBH 1500

** Homework Policies: **
The homework exercises are an essential part of this course
because practicing solving problems is important part of
understanding the material. You can probably find many of the
solutions to the homework exercises on the internet or in the
literature but you will not get the benefit of solving the problems
on your own. Therefore, the only sources you are allowed to consult
in solving these problems are the recommended texts listed below, and notes from class
(either mine, yours, or those of another student).

I encourage you to work in small groups, but you must note your collaborators on the homework you turn in. In addition, you must write up your own solutions without any collaboration.

You may elect to take a two-day extension (until Friday 5PM) on one of the homework assignments. Other assignments turned in late (but before Friday 5PM) will receive half credit.

You are also encouraged to put your solutions into LaTeX. Here is a template that you can use: Homework Template .

** Midterm and Final Policies: **
The midterm and final will be identical in format to the homework assignments,
except that they will be cumulative, and you must do your work individually. In addition, no late work is
accepted for the midterm or final.

** Evaluation and Grades: **
The midterm and final exam are each worth 15% of your final grade. Each of the seven homework assignments is
worth 10% of your final grade.

Most of the material for this class, including homework problems, came from Chris Umans' class in complexity theory at Caltech:

I will provide my own course notes before every lecture (although not necessarily very much in advance). When they are posted, you can reach them by clicking on the topic name in the course outline below. This is theoretically all you should need for understanding the material in class. However, you may wish to consult my sources in preparing these notes. These are:

Computational Complexity, by Christos Papadimitriou, Addison Wesley, 1993, ISBN: 978-0201530827Computational Complexity: A Modern Approach, by Arora and Barak, Cambridge University Press, 2009, ISBN: 978-0521424264

The list of topics is tentative for now.

Week | Topic | Homework | Class notes |
---|---|---|---|

Week 1 |
Languages, Turing Machines, Reductions, Completeness, Hierarchy Theorems, Complexity Classes |
Homework 1 HW1 Solutions |
Mon, Wed, Fri |

Week2 | Non-determinism, Part 1 Non-determinism, Part 2 |
Homework 2 HW2 Solutions |
Mon, Wed, Fri |

Week 3 |
Non-deterministic Space Circuits, non-uniformity |
Homework 3 HW3 Solutions |
Mon, Wed, Fri |

Week 4 |
Randomness Randomized Complexity Classes |
Homework 4 HW4 Solutions |
Mon, Wed, Fri |

Week 5 | - | - | - |

Week 6 | Alternation and the Polynomial Hierarchy |
Midterm Midterm Solutions |
Mon, Wed, Fri |

Week 7 | Complexity of Counting |
Homework 5 HW5 Solutions |
Mon, Wed, Fri |

Week 8 | Interactive proof systems |
Homework 6 HW6 Solutions |
Fri |

Week 9 |
PCPs and hardness of approximation PCPs and hardness of approximation, cont. |
- | Wed Fri |

Week 10 | NP in PCP(poly,1) | Final Exam | Wed Fri |