Compilation and Fast Model Counting beyond CNF

Alexis de Colnet; Stefan Szeider; Tianwei Zhang

doi:10.24963/ijcai.2024/367

Home/Archive/arXiv

arXiv · 2502.00434

Compilation and Fast Model Counting beyond CNF

Alexis de Colnet·Stefan Szeider·Tianwei Zhang

View original source ↗Read source document ↗Export metadata ↓

Abstract

Circuits in deterministic decomposable negation normal form (d-DNNF) are representations of Boolean functions that enable linear-time model counting. This paper strengthens our theoretical knowledge of what classes of functions can be efficiently transformed, or compiled, into d-DNNF. Our main contribution is the fixed-parameter tractable (FPT) compilation of conjunctions of specific constraints parameterized by incidence treewidth. This subsumes the known result for CNF. The constraints in question are all functions representable by constant-width ordered binary decision diagrams (OBDDs) for all variable orderings. For instance, this includes parity constraints and cardinality constraints with constant threshold. The running time of the FPT compilation is singly exponential in the incidence treewidth but hides large constants in the exponent. To balance that, we give a more efficient FPT algorithm for model counting that applies to a sub-family of the constraints and does not require compilation.

Explore related subjects

cs.CC cs.AI cs.LO

Keep this discovery

BibTeX RIS

Alexis de Colnet, Stefan Szeider, Tianwei Zhang. 2025-02-01. Compilation and Fast Model Counting beyond CNF. https://doi.org/10.24963/ijcai.2024%2F367

Cite the original work for its findings. Save a collection to share your selection of sources.

KEEP EXPLORING

Related papers

arXiv2026

The Computational Complexity of Holant Problems on 4-regular Graphs from the Stable Subgroup Sequence of $SL(2,\mathbb{C})$

The Holant framework provides a general setting for studying counting problems and includes graph homomorphisms (\#GH) and counting constraint satisfaction problems (\#CSP) as special cases. Over the past twenty years, a series of computational complexity dichotomies have been established for Holant problems, but the classification for complex-valued signatures is still open. The main obstacle is the case in which all signatures have even arity. In this paper, we establish a dichotomy for Holant problems with a complex-valued 4-ary signature, which is a key base case for the full classification of Holant problems. We present a new strategy by introducing Schur's theorem, the classification of finite subgroups of $\mathrm{SL}(2,\mathbb{C})$ and stable subgroup sequences into the proof. These new techniques are of independent interest.

cs.CC↗

arXiv2026

Max Independent Set Remains NP-hard when Excluding a Planar Induced Minor

We show that there is a fixed planar graph $H$, namely the $5 \times 5$ grid, such that Max Independent Set remains NP-hard in $H$-induced-minor-free graphs. This refutes the Dallard--Milani\v{c}--\v{S}torgel conjecture and a weakening of it by Gartland and Lokshtanov, and by Korhonen.

cs.CC↗

arXiv2026

Topology inside NC$^1$

We show that ACC$^0$ is precisely what can be computed with constant-width circuits of polynomial size and polylogarithmic genus. This extends a characterization given by Hansen, showing that planar constant-width circuits also characterize ACC$^0$. Thus polylogarithmic genus provides no additional computational power in this model. We consider other generalizations of planarity, including crossing number and thickness. We show that constant-width circuits of polynomial size and thickness two already suffice to capture all of NC$^1$.

cs.CC↗