2 Search Results for "Domshlak, Carmel"

Document
DOI: 10.4230/LIPIcs.SAT.2025.9
CNFs and DNFs with Exactly k Solutions

Authors: L. Sunil Chandran, Rishikesh Gajjala, and Kuldeep S. Meel

Published in: LIPIcs, Volume 341, 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)

Abstract
Model counting is a fundamental problem that consists of determining the number of satisfying assignments for a given Boolean formula. The weighted variant, which computes the weighted sum of satisfying assignments, has extensive applications in probabilistic reasoning, network reliability, statistical physics, and formal verification. A common approach for solving weighted model counting is to reduce it to unweighted model counting, which raises an important question: What is the minimum number of terms (or clauses) required to construct a DNF (or CNF) formula with exactly k satisfying assignments? In this paper, we establish both upper and lower bounds on this question. We prove that for any natural number k, one can construct a monotone DNF formula with exactly k satisfying assignments using at most O(√{log k}log log k) terms. This construction represents the first o(log k) upper bound for this problem. We complement this result by showing that there exist infinitely many values of k for which any DNF or CNF representation requires at least Ω(log log k) terms or clauses. These results have significant implications for the efficiency of model counting algorithms based on formula transformations.
Cite as

L. Sunil Chandran, Rishikesh Gajjala, and Kuldeep S. Meel. CNFs and DNFs with Exactly k Solutions. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 9:1-9:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{chandran_et_al:LIPIcs.SAT.2025.9,
  author =	{Chandran, L. Sunil and Gajjala, Rishikesh and Meel, Kuldeep S.},
  title =	{{CNFs and DNFs with Exactly k Solutions}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{9:1--9:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-381-2},
  ISSN =	{1868-8969},
  year =	{2025},
  volume =	{341},
  editor =	{Berg, Jeremias and Nordstr\"{o}m, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2025.9},
  URN =		{urn:nbn:de:0030-drops-237433},
  doi =		{10.4230/LIPIcs.SAT.2025.9},
  annote =	{Keywords: Model counting, #SAT, Set Systems, Combinatorics}
}
Document
DOI: 10.4230/DagSemProc.09491.3
Landmarks, Critical Paths and Abstractions: What's the Difference Anyway?

Authors: Malte Helmert and Carmel Domshlak

Published in: Dagstuhl Seminar Proceedings, Volume 9491, Graph Search Engineering (2010)

Abstract
Current heuristic estimators for classical domain-independent planning are usually based on one of four ideas: delete relaxation, abstraction, critical paths, and, most recently, landmarks. Previously, these different ideas for deriving heuristic functions were largely unconnected. In my talk, I will show that these heuristics are in fact very closely related. Moreover, I will introduce a new admissible heuristic called the landmark cut heuristic which exploits this relationship. In our experiments, the landmark cut heuristic provides better estimates than other current admissible planning heuristics, especially on large problem instances.
Cite as

Malte Helmert and Carmel Domshlak. Landmarks, Critical Paths and Abstractions: What's the Difference Anyway?. In Graph Search Engineering. Dagstuhl Seminar Proceedings, Volume 9491, pp. 1-2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)

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@InProceedings{helmert_et_al:DagSemProc.09491.3,
  author =	{Helmert, Malte and Domshlak, Carmel},
  title =	{{Landmarks, Critical Paths and Abstractions: What's the Difference Anyway?}},
  booktitle =	{Graph Search Engineering},
  pages =	{1--2},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{9491},
  editor =	{Lubos Brim and Stefan Edelkamp and Erik A. Hansen and Peter Sanders},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.09491.3},
  URN =		{urn:nbn:de:0030-drops-24324},
  doi =		{10.4230/DagSemProc.09491.3},
  annote =	{Keywords: Planning, heuristic search, heuristic functions}
}
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