Counting CSP Solutions Using Generalized XOR Constraints

We present a general framework for determining the number of solutions of constraint satisfaction problems (CSPs) with a high precision. Our first strategy uses additional binary variables for the CSP, and applies an XOR or parity constraint based method introduced previously for Boolean satisfiability (SAT) problems. In the CSP framework, in addition to the naive individual filtering of XOR constraints used in SAT, we are able to apply a global domain filtering algorithm by viewing these constraints as a collection of linear equalities over the field of two elements. Our most promising strategy extends this approach further to larger domains, and applies the so-called generalized XOR constraints directly to CSP variables. This allows us to reap the benefits of the compact and structured representation that CSPs offer. We demonstrate the effectiveness of our counting framework through experimental comparisons with the solution enumeration approach (which, we believe, is the curr...

• Type: Conference
• Year: 2007
• Where: AAAI
• Authors: Carla P. Gomes, Willem Jan van Hoeve, Ashish Sabharwal, Bart Selman
• Keywords: AAAI 2007, Generalized Xor Constraints, Intelligent Agents, Solution Counting, XOR Constraints