Symbolic Uniform Sampling with XOR Circuits

Uniform sampling is an important method in statistics and has various applications in model counting, system verification, algorithm design, among others. Symbolic sampling in a Boolean space is a recently proposed technique that combines sampling and symbolic representation for effective Boolean reasoning. Under the framework of symbolic sampling, we propose a method to construct compact XOR circuits achieving uniform sampling in a given Boolean space. The method is further extended to biased sampling within a focused subspace of interest. Experimental results show the effectiveness of compact sampling circuit generation and its potential to facilitate Boolean reasoning.