# 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!

• 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