Search Results

Documents authored by de Colnet, Alexis

Document
DOI: 10.4230/LIPIcs.SAT.2026.13
The Compilability Thresholds of 2-CNF to OBDD

Authors: Alexis de Colnet, Alfons Laarman, and Joon Hyung Lee

Published in: LIPIcs, Volume 377, 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)

Abstract
We prove the existence of two thresholds regarding the compilability of random 2-CNF formulas to OBDDs. The formulas are drawn from F₂(n,δn), the uniform distribution over all 2-CNFs with δ n clauses and n variables, with δ ≥ 0 a constant. We show that, with high probability, the random 2-CNF admits OBDDs of size polynomial in n if 0 ≤ δ < 1/2 or if δ > 1. On the other hand, for 1/2 < δ < 1, with high probability, the random 2-CNF admits only OBDDs of size exponential in n. It is no coincidence that the two "compilability thresholds" are δ = 1/2 and δ = 1. Both are known thresholds for other CNF properties, namely, δ = 1 is the satisfiability threshold for 2-CNF while δ = 1/2 is the treewidth threshold, i.e., the point where the treewidth of the primal graph jumps from constant to linear in n with high probability.
Cite as

Alexis de Colnet, Alfons Laarman, and Joon Hyung Lee. The Compilability Thresholds of 2-CNF to OBDD. In 29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026). Leibniz International Proceedings in Informatics (LIPIcs), Volume 377, pp. 13:1-13:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2026)

Copy BibTex To Clipboard

@InProceedings{decolnet_et_al:LIPIcs.SAT.2026.13,
  author =	{de Colnet, Alexis and Laarman, Alfons and Lee, Joon Hyung},
  title =	{{The Compilability Thresholds of 2-CNF to OBDD}},
  booktitle =	{29th International Conference on Theory and Applications of Satisfiability Testing (SAT 2026)},
  pages =	{13:1--13:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-431-4},
  ISSN =	{1868-8969},
  year =	{2026},
  volume =	{377},
  editor =	{Ignatiev, Alexey and Szeider, Stefan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2026.13},
  URN =		{urn:nbn:de:0030-drops-263190},
  doi =		{10.4230/LIPIcs.SAT.2026.13},
  annote =	{Keywords: Knowledge Compilation, OBDD, Random CNF, Phase Transition}
}
Document
DOI: 10.4230/LIPIcs.ICDT.2025.30
An FPRAS for Model Counting for Non-Deterministic Read-Once Branching Programs

Authors: Kuldeep S. Meel and Alexis de Colnet

Published in: LIPIcs, Volume 328, 28th International Conference on Database Theory (ICDT 2025)

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.
Cite as

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)

Copy BibTex To Clipboard

@InProceedings{meel_et_al:LIPIcs.ICDT.2025.30,
  author =	{Meel, Kuldeep S. and de Colnet, Alexis},
  title =	{{An FPRAS for Model Counting for Non-Deterministic Read-Once Branching Programs}},
  booktitle =	{28th International Conference on Database Theory (ICDT 2025)},
  pages =	{30:1--30:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-364-5},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{328},
  editor =	{Roy, Sudeepa and Kara, Ahmet},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICDT.2025.30},
  URN =		{urn:nbn:de:0030-drops-229717},
  doi =		{10.4230/LIPIcs.ICDT.2025.30},
  annote =	{Keywords: Approximate model counting, FPRAS, Knowledge compilation, nFBDD}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.11
On the Relative Efficiency of Dynamic and Static Top-Down Compilation to Decision-DNNF

Authors: Alexis de Colnet

Published in: LIPIcs, Volume 305, 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)

Abstract
Top-down compilers of CNF formulas to circuits in decision-DNNF (Decomposable Negation Normal Form) have proved to be useful for model counting. These compilers rely on a common set of techniques including DPLL-style exploration of the set of models, caching of residual formulas, and connected components detection. Differences between compilers lie in the variable selection heuristics and in the additional processing techniques they may use. We investigate, from a theoretical perspective, the ability of top-down compilation algorithms to find small decision-DNNF circuits for two different variable selection strategies. Both strategies are guided by a graph of the CNF formula and are inspired by what is done in practice. The first uses a dynamic graph-partitioning approach while the second works with a static tree decomposition. We show that the dynamic approach performs significantly better than the static approach for some formulas, and that the opposite also holds for other formulas. Our lower bounds are proved despite loose settings where the compilation algorithm is only forced to follow its designed variable selection strategy and where everything else, including the many opportunities for tie-breaking, can be handled non-deterministically.
Cite as

Alexis de Colnet. On the Relative Efficiency of Dynamic and Static Top-Down Compilation to Decision-DNNF. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 11:1-11:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

Copy BibTex To Clipboard

@InProceedings{decolnet:LIPIcs.SAT.2024.11,
  author =	{de Colnet, Alexis},
  title =	{{On the Relative Efficiency of Dynamic and Static Top-Down Compilation to Decision-DNNF}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{11:1--11:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-334-8},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{305},
  editor =	{Chakraborty, Supratik and Jiang, Jie-Hong Roland},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2024.11},
  URN =		{urn:nbn:de:0030-drops-205339},
  doi =		{10.4230/LIPIcs.SAT.2024.11},
  annote =	{Keywords: Knowledge compilation, top-down compilation, decision-DNNF Circuits}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.7
Separating Incremental and Non-Incremental Bottom-Up Compilation

Authors: Alexis de Colnet

Published in: LIPIcs, Volume 271, 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)

Abstract
The aim of a compiler is, given a function represented in some language, to generate an equivalent representation in a target language L. In bottom-up (BU) compilation of functions given as CNF formulas, constructing the new representation requires compiling several subformulas in L. The compiler starts by compiling the clauses in L and iteratively constructs representations for new subformulas using an "Apply" operator that performs conjunction in L, until all clauses are combined into one representation. In principle, BU compilation can generate representations for any subformulas and conjoin them in any way. But an attractive strategy from a practical point of view is to augment one main representation - which we call the core - by conjoining to it the clauses one at a time. We refer to this strategy as incremental BU compilation. We prove that, for known relevant languages L for BU compilation, there is a class of CNF formulas that admit BU compilations to L that generate only polynomial-size intermediate representations, while their incremental BU compilations all generate an exponential-size core.
Cite as

Alexis de Colnet. Separating Incremental and Non-Incremental Bottom-Up Compilation. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 7:1-7:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

Copy BibTex To Clipboard

@InProceedings{decolnet:LIPIcs.SAT.2023.7,
  author =	{de Colnet, Alexis},
  title =	{{Separating Incremental and Non-Incremental Bottom-Up Compilation}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{7:1--7:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-286-0},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{271},
  editor =	{Mahajan, Meena and Slivovsky, Friedrich},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2023.7},
  URN =		{urn:nbn:de:0030-drops-184696},
  doi =		{10.4230/LIPIcs.SAT.2023.7},
  annote =	{Keywords: Knowledge Compilation, Bottom-up Compilation, DNNF, OBDD}
}
Any Issues?
X

Feedback on the Current Page

CAPTCHA

Thanks for your feedback!

Feedback submitted to Dagstuhl Publishing

Could not send message

Please try again later or send an E-mail
© 2023-2026 Schloss Dagstuhl – LZI GmbH Schloss Dagstuhl – LZI GmbH About DROPS Imprint Privacy Contact