Projected Model Counting
This work addresses a specific problem in probabilistic reasoning and SAT solving, presenting incremental improvements with new methods for projected model counting.
The paper tackles the problem of projected model counting, which involves counting assignments to a subset of priority variables that can be extended to satisfy a propositional theory, addressing scenarios where some variables are irrelevant. It introduces three approaches, including two novel ones, and compares their performance on benchmark problems.
Model counting is the task of computing the number of assignments to variables V that satisfy a given propositional theory F. Model counting is an essential tool in probabilistic reasoning. In this paper, we introduce the problem of model counting projected on a subset P of original variables that we call 'priority' variables. The task is to compute the number of assignments to P such that there exists an extension to 'non-priority' variables V¶that satisfies F. Projected model counting arises when some parts of the model are irrelevant to the counts, in particular when we require additional variables to model the problem we are counting in SAT. We discuss three different approaches to projected model counting (two of which are novel), and compare their performance on different benchmark problems. To appear in 18th International Conference on Theory and Applications of Satisfiability Testing, September 24-27, 2015, Austin, Texas, USA