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Towards Practical First-Order Model Counting.
Ananth K. Kidambi, Guramrit Singh, Paulius Dilkas and Kuldeep S. Meel.
In Proceedings of the International Conference on Theory and Applications of Satisfiability Testing (SAT), pp. 18:1–18:18, August 2025.
First-order model counting (FOMC) is the problem of counting the number of models of a sentence in first-order logic. Since lifted inference techniques rely on reductions to variants of FOMC, the design of scalable methods for FOMC has attracted attention from both theoreticians and practitioners over the past decade. Recently, a new approach based on first-order knowledge compilation was proposed. This approach, called Crane, instead of simply providing the final count, generates definitions of (possibly recursive) functions that can be evaluated with different arguments to compute the model count for any domain size. However, this approach is not fully automated, as it requires manual evaluation of the constructed functions. The primary contribution of this work is a fully automated compilation algorithm, called Crane2, which transforms the function definitions into C++ code equipped with arbitrary-precision arithmetic. These additions allow the new FOMC algorithm to scale to domain sizes over 500,000 times larger than the current state of the art, as demonstrated through experimental results.
@inproceedings{KSDM25,
title={Towards Practical First-Order Model Counting},
author={
Kidambi, Ananth K. and Singh, Guramrit and Dilkas, Paulius and Meel, Kuldeep
S.
},
booktitle=SAT,
pages={18:1--18:18},
year={2025},
month=aug,
bib2html_rescat={Counting},
bib2html_pubtype={Refereed Conference},
bib2html_dl_pdf=
{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.18},
abstract={
First-order model counting (FOMC) is the problem of counting the number of
models of a sentence in first-order logic. Since lifted inference techniques
rely on reductions to variants of FOMC, the design of scalable methods for
FOMC has attracted attention from both theoreticians and practitioners over
the past decade. Recently, a new approach based on first-order knowledge
compilation was proposed. This approach, called Crane, instead of simply
providing the final count, generates definitions of (possibly recursive)
functions that can be evaluated with different arguments to compute the
model count for any domain size. However, this approach is not fully
automated, as it requires manual evaluation of the constructed functions.
The primary contribution of this work is a fully automated compilation
algorithm, called Crane2, which transforms the function definitions into C++
code equipped with arbitrary-precision arithmetic. These additions allow the
new FOMC algorithm to scale to domain sizes over 500,000 times larger than
the current state of the art, as demonstrated through experimental results.
},
}
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