Sampling Combinatorial Spaces Using Biased Random Walks

For probabilistic reasoning, one often needs to sample from a combinatorial space. For example, one may need to sample uniformly from the space of all satisfying assignments. Can state-of-the-art search procedures for SAT be used to sample effectively from the space of all solutions? And, if so, how uniformly do they sample? Our initial results find that on the positive side, one can find all solutions to a given instance. Nevertheless, sampling can be highly biased. This research provides a starting point for the development of more balanced procedures.