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An FPRAS for Model Counting for Non-Deterministic Read-Once Branching Programs

Authors Kuldeep S. Meel , Alexis de Colnet

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  • Theory of computation → Approximation algorithms analysis
Keywords
  • Approximate model counting
  • FPRAS
  • Knowledge compilation
  • nFBDD

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Abstract

Non-deterministic read-once branching programs, also known as non-deterministic free binary decision diagrams (nFBDD), are a fundamental data structure in computer science for representing Boolean functions. In this paper, we focus on #nFBDD, the problem of model counting for non-deterministic read-once branching programs. The #nFBDD problem is #P-hard, and it is known that there exists a quasi-polynomial randomized approximation scheme for #nFBDD. In this paper, we provide the first FPRAS for #nFBDD. Our result relies on the introduction of new analysis techniques that focus on bounding the dependence of samples.

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Kuldeep S. Meel and Alexis de Colnet. An FPRAS for Model Counting for Non-Deterministic Read-Once Branching Programs. In 28th International Conference on Database Theory (ICDT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 328, pp. 30:1-30:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025) https://doi.org/10.4230/LIPIcs.ICDT.2025.30

Author Details

Kuldeep S. Meel
  • University of Toronto, Canada
Alexis de Colnet
  • TU Wien, Austria

Funding

Meel acknowledges the support of the Natural Sciences and Engineering Research Council of Canada (NSERC), funding reference number RGPIN-2024-05956; de Colnet is supported by the Austrian Science Fund (FWF), ESPRIT project FWF ESP 235. This work was done in part while de Colnet was visiting the University of Toronto.

Acknowledgements

This research was initiated at Dagstuhl Seminar 24171 on "Automated Synthesis: Functional, Reactive and Beyond" (https://www.dagstuhl.de/24171). We gratefully acknowledge the Schloss Dagstuhl - Leibniz Center for Informatics for providing an excellent environment and support for scientific collaboration.

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