CPSC 433: Search example

	Rob Kremer
	Search Samples: Constrain Satisfaction CPSC 433: Artificial Intelligence	Computer Science

Problem Description:

A constraint satisfaction problem (CSP) consists of
a set X = {X₁,…,X_n} of variables over some finite, discrete-valued domains D = {D₁,…,D_n} and
a set of constraints C = {C₁,…,C_m}. Each constraint C_i is a relation over the domains of a subset of the variables, i.e.? C_i = R_i(X_i,1,…,X_i,k)?where the relation R_i describes every value-tuple in D_i,1×…×D_i,k that fulfills the constraint.
The problem is to find a value for each X_j (out of its ?D_j) that fulfills all C_i.

Give a fully-specified formal model and process for an arbitrary CSP.

Also give a fully-specified formal search instance for the following two problems:

X = {X₁,X₂}?
   D₁ = {1,2,3}
   D₂ = {1,2,3,4}
?C = {C₁,C₂,C₃}
? C₁: X₁ + X₂ ≤ 4
C₂: X₁ + X₂ ≥ 3
C₃: X₁ ≥ 2

X = {X₁,X₂,X₃}
? D₁ = D₂ = D₃ = {true, false}?
C = {C₁,C₂,C₃}?
   C₁: X₁ ∨ ¬X₂ ∨ X₃
   C₂: ¬X₁ ∨ X₃
   C₃: ¬X₂ ∨ ¬X₃

CPSC 433: Artificial Intelligence

Last updated 2013-08-31 00:00

Rob Kremer