# Answer Set Counting and its Applications

arXiv: https://arxiv.org/abs/2502.09231 · HTML: https://mlsanity.com/paper/2502.09231/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Builds on 10 of its 42 references that are in the map.
- First posted on arXiv 13 Feb 2025.

## Builds on (most cited first, 10 of 10)

- [A Scalable Approximate Model Counter](https://mlsanity.com/paper/1306.5726/) (2013)
- [Answer Set Solving with Bounded Treewidth Revisited](https://mlsanity.com/paper/1702.02890/) (2017)
- [Rushing and Strolling among Answer Sets -- Navigation Made Easy](https://mlsanity.com/paper/2112.07596/) (2021)
- [Stable Model Counting and Its Application in Probabilistic Logic Programming](https://mlsanity.com/paper/1411.5410/) (2014)
- [Partition Function Estimation: A Quantitative Study](https://mlsanity.com/paper/2105.11132/) (2021)
- [On the Tractability of Minimal Model Computation for Some CNF Theories](https://mlsanity.com/paper/1310.8120/) (2013)
- [Synthesis of Boolean Networks from Biological Dynamical Constraints using Answer-Set Programming](https://mlsanity.com/paper/1909.04309/) (2019)
- [Exact ASP Counting with Compact Encodings](https://mlsanity.com/paper/2312.11936/) (2023)
- [On Lower Bounding Minimal Model Count](https://mlsanity.com/paper/2407.09744/) (2024)
- [IASCAR: Incremental Answer Set Counting by Anytime Refinement](https://mlsanity.com/paper/2311.07233/) (2023)

## Abstract (arXiv)

We have focused on Answer Set Programming (ASP), more specifically, answer set counting, exploring both exact and approximate methodologies. We developed an exact ASP counter, sharpASP, which utilizes a compact encoding for propositional formulas, significantly enhancing efficiency compared to existing methods that often struggle with inefficient encodings. Our evaluations indicate that sharpASP outperforms current ASP counters on several benchmarks. In addition, we proposed an approximate ASP counter, named ApproxASP, a hashing-based counter integrating Gauss-Jordan elimination within the ASP solver, clingo. As a practical application, we employed ApproxASP for network reliability estimation, demonstrating superior performance over both traditional reliability estimators and #SAT-based methods.