## Computer Science and Engineering, Department of

# Towards a Definition of the Constraint Probability of Non-Binary Constraint Networks

**Document Type** Article

Published in Working Note of the Constraint Systems Laboratory (UNL). Published Nov. 28, 2003.

#### Abstract

The constraint probability of a constraint network is the ratio of the number of constraints in the network over that of all possible constraints. While this parameter can be easily computed for binary networks, it is not clear how to compute it for non-binary networks. In a non-binary network, a constraint *C _{x}* of arity

*k*induces constraints between any combination of the variables in the scope of

*C*. These induced constraints need to be taken into consideration when computing the constraint probability of a non-binary network. In this report we propose a method for computing the constraint probability of a non-binary Constraint Network (CN), and illustrate the use of this new definition on a simple example.

_{x}*This paper has been withdrawn.*