1. CSC 380: Design and Analysis of Algorithms
Dr. Curry Guinn

2. Quick Info Dr. Curry Guinn CIS 2015 guinnc@uncw.edu
Office Hours: MWF: 10:00am-11:00m and by appointment

3. Outline of today Satisfiability 3-SAT What’s the problem?
How would we code this problem?

4. The Satisfiability Problem
Given a set of propositional logic clauses, find an assignment of truth values to each symbol so that all of the clauses are true.
(P -> Q & S) & (~P & ~Q) & (S | ~Q)

5. 3SAT is a special case All clauses contain the disjunction of 3 terms
Disjunction means OR
Each term is of the form P or ~P.
(P | Q | ~S) & (~P | ~Q | ~S) & (P | ~Q | S)
It turns out that any SAT case, can be transformed into 3SAT

6. 3SAT is an NP-complete problem
Which means that it is map-able to other NP-complete problems such as
Traveling salesman
Clique
Map coloring
Knapsack,
Etc.
What do I mean by “map-able”?

7. Suppose we want to actually write code to solve this problem
How do we do it?
Analysis
Design
Implement
Test

8. Analysis
Can we write down the problem?

9. Write down the problem
Find a set of truth assignments for the propositional symbols such that are of the clauses are true. Each clause consist of a disjunction (OR) of three terms. Each term is either a proposition symbol or its negation (i.e., P or ~P).
More generally, for a particular problem, we will have n different propositional symbols and m different clauses.
Do you want to add anything?

10. Find the nouns. Why?

11. Find the nouns. Why?
Find a set of truth assignments for the propositional symbols such that all of the clauses are true. Each clause consist of a disjunction (OR) of three terms. Each term is either a proposition symbol or its negation (i.e., P or ~P).
More generally, for a particular problem, we will have n different propositional symbols and m different clauses.

12. Start making UML diagrams of the classes
Term
Clause
Symbol
TruthAssignment
Problem

13. See board and IDE

14. For Next Class, Monday
No Homework
Enjoy the weekend