# Golden Ticket: Chapter 4

## Optional Get-Together

- When: Tonight at 7:00 p.m.
- Where: 721 South 6th Avenue
- What: Watch CodeBreaker,
a movie about Alan Turing.
- What: Play games such as
**CSCI 338 Charades**.
If you have a fun game that works in a group setting, bring it along!
- Munchies: Pizza and soda!

## For Your Enjoyment

- There is an annual competition
to identify new benchmarks and promote new approaches
to the satisfiability problem.

## The Hardest Problems in NP

- In 1971, Steve Cook proved that the
satisfiability
problem is the hardest type of NP problem.
- Since then, many other NP problems have been shown to be equivalent
to satisfiability.
- These problems are called
**NP-Complete** (NPC) problems.
- To demonstrate that Problem X is NPC, (1) show that Problem X is in NP and
(2) show a polynomial reduction from a known NPC problem to Problem X.
(We will learn more about this in section 7.4 of the Sipser book.)
- Sudoku is NP-complete.
- Minesweeper is NP-complete.
- Tetris is NP-complete.
- The Traveling Salesperson Problem is NP-complete.
- The Bin Packing Problem is NP-complete.
- The status of some problems is unknown. For example, graph
isomorphism and factoring are both believed to be harder than
P but easier than NPC.

## Active Learning Problem

Model the following statements as a satisfiability problem.
What is the solution?

- Qing can only meet on Monday, Wednesday or Thursday
- Upulee can't meet on Wednesday
- Hunter can't meet on either Tuesday or Friday

## Active Learning Problem

Model the following Frenemy statements as a satisfiability problem
that enables friendship cliques to be identified.

- Mike and Binhai are friends
- Brittany and Brendan are friends
- Binhai and Brendan are friends