CCDD: A Tractable Representation for Model Counting and Uniform Sampling

TL;DR

This paper introduces CCDD, a new representation language for model counting and uniform sampling that enables polytime queries and outperforms existing methods in compilation and problem-solving efficiency.

Contribution

We propose CCDD, a novel representation language with restrictions on conjunction nodes, supporting efficient model counting and sampling, and demonstrate its superior performance over existing approaches.

Findings

CCDD supports polytime model counting and sampling.

Our compiler produces smaller representations than state-of-the-art methods.

Empirical results show increased problem-solving instances with CCDD.

Abstract

Knowledge compilation concerns with the compilation of representation languages to target languages supporting a wide range of tractable operations arising from diverse areas of computer science. Tractable target compilation languages are usually achieved by restrictions on the internal nodes of the NNF. In this paper, we propose a new representation language CCDD, which introduces new restrictions on conjunction nodes to capture equivalent literals. We show that CCDD supports two key queries, model counting and uniform samping, in polytime. We present algorithms and a compiler to compile propositional formulas expressed in CNF into CCDD. Experiments over a large set of benchmarks show that our compilation times are better with smaller representation than state-of-art Decision-DNNF, SDD and OBDD[AND] compilers. We apply our techniques to model counting and uniform sampling, and develop model counter and uniform sampler on CNF. Our empirical evaluation demonstrates the following significant improvements: our model counter can solve 885 instances while the prior state of the art solved only 843 instances, representing an improvement of 43 instances; and our uniform sampler can solve 780 instances while the prior state of the art solved only 648 instances, representing an improvement of 132 instances.