Short XORs for model counting: from theory to practice

Authors:
Carla P. Gomes;Joerg Hoffmann;Ashish Sabharwal;Bart Selman
Affiliations:
Dept. of Computer Science, Cornell University, Ithaca, NY;University of Innsbruck, Innsbruck, Austria;Dept. of Computer Science, Cornell University, Ithaca, NY;Dept. of Computer Science, Cornell University, Ithaca, NY
Venue:
SAT'07 Proceedings of the 10th international conference on Theory and applications of satisfiability testing
Year:
2007

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Abstract

A promising approach for model counting was recently introduced, which in theory requires the use of large random XOR or parity constraints to obtain near-exact counts of solutions to Boolean formulas. In practice, however, short XOR constraints are preferred as they allow better constraint propagation in SAT solvers. We narrow this gap between theory and practice by presenting experimental evidence that for structured problem domains, very short XOR constraints can lead to probabilistic variance as low as large XOR constraints, and thus provide the same correctness guarantees. We initiate an understanding of this phenomenon by relating it to structural properties of synthetic instances.