{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

Lecture06 - CS440/ECE448 Intro to Articial Intelligence...

Info icon This preview shows pages 1–10. Sign up to view the full content.

View Full Document Right Arrow Icon
Lecture 6: More on constraint satisfaction problems Prof. Julia Hockenmaier [email protected] http://cs.illinois.edu/fa11/cs440 CS440/ECE448: Intro to Artificial Intelligence
Image of page 1

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Tuesday ʼ s key concepts Constraint satisfaction problems: Given: a set of n variables X 1 ..X n , with domains (sets of possible values) D 1 …D n , and a set of m constraints C 1 … C m Task: assign a value from D i for each X i subjects to the constraints.
Image of page 2
CSP 1: Map coloring (Binary constraints)
Image of page 3

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Map coloring: a solution for N=3 4 CS440/ECE448: Intro AI
Image of page 4
Constraint satisfaction problems are defined by… - a set of variables X : {WA, NT, QLD, NSW, VA, SA, TA} - a set of domains D i (possible values for variable x i ): D WA = {red, blue, green} - a set of constraints C : { (WA,NT) , WA NT , (WA,QLD), WA QLD ,…} scope relation 5 CS440/ECE448: Intro AI
Image of page 5

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
States and solutions Each state is a complete or partial assignment of values to variables: state35 = {WA=red, NT=blue, QLD= green, NSW= red, VA= green, SA= blue, TA= red}; state23 = {WA = red} Legal assignments don ʼ t violate any constraints. Solutions are complete legal assignments 6 CS440/ECE448: Intro AI
Image of page 6
Binary constraints: constraint graph QLD NT NSW VA TA SA WA CS440/ECE448: Intro AI 7
Image of page 7

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Consistency Node consistency: X is node-consistent iff each element in D X satisfies unary constraints on X Arc consistency: X is arc-consistent iff for each C(X, Y) and for each x D X there is a y D Y such that the assignment {X=x, Y=y} satisfies C(X,Y). Path consistency: {X,Y} are path consistent wrt. Z iff for every x D X and y D X there is a z D Z such that the assignment {X=x,Y=y,Z=z} satisfies C(X,Z) and C(Y,Z) 8 CS440/ECE448: Intro AI
Image of page 8
AC-3 // Is the CSP c arc-consistent? function AC3(CSP c) input: CSP c = (X,D,C) local: queue q all arcs C(X,Y) in c while q () do: // Can C(X,Y) be satisfied?
Image of page 9

Info icon This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document Right Arrow Icon
Image of page 10
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

What students are saying

  • Left Quote Icon

    As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

    Student Picture

    Kiran Temple University Fox School of Business ‘17, Course Hero Intern

  • Left Quote Icon

    I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

    Student Picture

    Dana University of Pennsylvania ‘17, Course Hero Intern

  • Left Quote Icon

    The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

    Student Picture

    Jill Tulane University ‘16, Course Hero Intern