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Documents authored by Nadel, Alexander

Document
DOI: 10.4230/LIPIcs.SAT.2025.22
Enumerating All Boolean Matches

Authors: Alexander Nadel and Yogev Shalmon

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

Abstract
Boolean matching, a fundamental problem in circuit design, determines whether two Boolean circuits are equivalent under input/output permutations and negations. While most works focus on finding a single match or proving its absence, the problem of enumerating all matches remains largely unexplored, with BooM being a notable exception. Motivated by timing challenges in Intel’s library mapping flow, we introduce EBat - an open-source tool for enumerating all matches between single-output circuits. Built from scratch, EBat reuses BooM’s SAT encoding and introduces novel high-level algorithms and performance-critical subroutines to efficiently identify and block multiple mismatches and matches simultaneously. Experiments demonstrate that EBat substantially outperforms BooM’s baseline algorithm, solving 3 to 4 times more benchmarks within a given time limit. EBat has been productized as part of Intel’s library mapping flow, effectively addressing the timing challenges.
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Alexander Nadel and Yogev Shalmon. Enumerating All Boolean Matches. In 28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025). Leibniz International Proceedings in Informatics (LIPIcs), Volume 341, pp. 22:1-22:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2025)

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@InProceedings{nadel_et_al:LIPIcs.SAT.2025.22,
  author =	{Nadel, Alexander and Shalmon, Yogev},
  title =	{{Enumerating All Boolean Matches}},
  booktitle =	{28th International Conference on Theory and Applications of Satisfiability Testing (SAT 2025)},
  pages =	{22:1--22:21},
  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.2025.22},
  URN =		{urn:nbn:de:0030-drops-237568},
  doi =		{10.4230/LIPIcs.SAT.2025.22},
  annote =	{Keywords: Boolean Matching, All-Boolean-Matching, Enumeration, SAT, Generalization}
}
Document
DOI: 10.4230/LIPIcs.SAT.2024.13
Entailing Generalization Boosts Enumeration

Authors: Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon

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

Abstract
Given a combinational circuit Γ with a single output o, AllSAT-CT is the problem of enumerating all solutions of Γ. Recently, we introduced several state-of-the-art AllSAT-CT algorithms based on satisfying generalization, which generalizes a given total Boolean solution to a smaller ternary solution that still satisfies the circuit. We implemented them in our open-source tool HALL. In this work we draw upon recent theoretical works suggesting that utilizing generalization algorithms, which can produce solutions that entail the circuit without satisfying it, may enhance enumeration. After considering the theory and adapting it to our needs, we enrich HALL’s AllSAT-CT algorithms by incorporating several newly implemented generalization schemes and additional SAT solvers. By conducting extensive experiments we show that entailing generalization substantially boosts HALL’s performance and quality (where quality corresponds to the number of reported generalized solutions per instance), with the best results achieved by combining satisfying and entailing generalization.
Cite as

Dror Fried, Alexander Nadel, Roberto Sebastiani, and Yogev Shalmon. Entailing Generalization Boosts Enumeration. In 27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 305, pp. 13:1-13:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{fried_et_al:LIPIcs.SAT.2024.13,
  author =	{Fried, Dror and Nadel, Alexander and Sebastiani, Roberto and Shalmon, Yogev},
  title =	{{Entailing Generalization Boosts Enumeration}},
  booktitle =	{27th International Conference on Theory and Applications of Satisfiability Testing (SAT 2024)},
  pages =	{13:1--13:14},
  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.2024.13},
  URN =		{urn:nbn:de:0030-drops-205351},
  doi =		{10.4230/LIPIcs.SAT.2024.13},
  annote =	{Keywords: Generalization, Minimization, Prime Implicant, AllSAT, SAT, Circuits}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.9
AllSAT for Combinational Circuits

Authors: Dror Fried, Alexander Nadel, and Yogev Shalmon

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

Abstract
Motivated by the need to improve the scalability of Intel’s in-house Static Timing Analysis (STA) tool, we consider the problem of enumerating all the solutions of a single-output combinational Boolean circuit, called AllSAT-CT. While AllSAT-CT is immediately reducible to enumerating the solutions of a Boolean formula in Conjunctive Normal Form (AllSAT-CNF), our experiments had shown that such a reduction, followed by applying state-of-the-art AllSAT-CNF tools, does not scale well on neither our industrial AllSAT-CT instances nor generic circuits, both when the user requires the solutions to be disjoint or when they can be non-disjoint. We focused on understanding the reasons for this phenomenon for the well-known iterative blocking family of AllSAT-CNF algorithms. We realized that existing blocking AllSAT-CNF algorithms fail to generalize efficiently for AllSAT-CT, since they are restricted to Boolean logic. Consequently, we introduce three dedicated AllSAT-CT algorithms that are ternary-logic-aware: a ternary simulation-based algorithm TALE, a dual-rail&MaxSAT-based algorithm MARS, and their combination. Specifically, we introduce in MARS two novel blocking clause generation approaches for the disjoint and non-disjoint cases. We implemented our algorithms in our new tool HALL. We show that HALL scales substantially better than any reduction to existing AllSAT-CNF tools on our industrial STA instances as well as on publicly available families of combinational circuits for both the disjoint and the non-disjoint cases.
Cite as

Dror Fried, Alexander Nadel, and Yogev Shalmon. AllSAT for Combinational Circuits. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 9:1-9:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{fried_et_al:LIPIcs.SAT.2023.9,
  author =	{Fried, Dror and Nadel, Alexander and Shalmon, Yogev},
  title =	{{AllSAT for Combinational Circuits}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{9:1--9:18},
  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.2023.9},
  URN =		{urn:nbn:de:0030-drops-184717},
  doi =		{10.4230/LIPIcs.SAT.2023.9},
  annote =	{Keywords: AllSAT, SAT, Circuits}
}
Document
DOI: 10.4230/LIPIcs.SAT.2023.17
Solving Huge Instances with Intel(R) SAT Solver

Authors: Alexander Nadel

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

Abstract
We introduce a new release of our SAT solver Intelregistered SAT Solver. The new release, called IS23, is targeted to solve huge instances beyond the capacity of other solvers. IS23 can use 64-bit clause-indices and store clauses compressedly using bit-arrays, where each literal is normally allocated fewer than 32 bits. As a preliminary result, we show that only IS23 can handle a gigantic trivially satisfiable instance with over 8.5 billion clauses. Then, we demonstrate that IS23 enables a significant improvement in the capacity of our industrial tool for cell placement in physical design, since only IS23 can solve placement instances with up to 4.3 billion clauses. Finally, we show that IS23 is substantially more efficient than other solvers for finding many (10⁶) placements on instances with up to 170 million clauses. We use the latter application to demonstrate that variable succession, that is, the order in which the variables are provided to the solver, might have a significant impact on IS23’s performance, thereby providing a new dimension to SAT encoding considerations.
Cite as

Alexander Nadel. Solving Huge Instances with Intel(R) SAT Solver. In 26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 271, pp. 17:1-17:12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{nadel:LIPIcs.SAT.2023.17,
  author =	{Nadel, Alexander},
  title =	{{Solving Huge Instances with Intel(R) SAT Solver}},
  booktitle =	{26th International Conference on Theory and Applications of Satisfiability Testing (SAT 2023)},
  pages =	{17:1--17:12},
  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.2023.17},
  URN =		{urn:nbn:de:0030-drops-184790},
  doi =		{10.4230/LIPIcs.SAT.2023.17},
  annote =	{Keywords: SAT, CDCL}
}
Document
DOI: 10.4230/LIPIcs.SAT.2022.8
Introducing Intel(R) SAT Solver

Authors: Alexander Nadel

Published in: LIPIcs, Volume 236, 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)

Abstract
We introduce Intel(R) SAT Solver (IntelSAT) - a new open-source CDCL SAT solver, written from scratch. IntelSAT is optimized for applications which generate many mostly satisfiable incremental SAT queries. We apply the following Incremental Lazy Backtracking (ILB) principle: in-between incremental queries, backtrack only when necessary and to the highest possible decision level. ILB is enabled by a novel reimplication procedure, which can reimply an assigned literal at a lower level without backtracking. Reimplication also helped us to restore the following two properties, lost in the modern solvers with the introduction of chronological backtracking: no assigned literal can be implied at a lower level, conflict analysis always starts with a clause falsified at the lowest possible level. In addition, we apply some new heuristics. Integrating IntelSAT into the MaxSAT solver TT-Open-WBO-Inc resulted in a significant performance boost on incomplete unweighted MaxSAT Evaluation benchmarks and improved the state-of-the-art in anytime unweighted MaxSAT solving.
Cite as

Alexander Nadel. Introducing Intel(R) SAT Solver. In 25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022). Leibniz International Proceedings in Informatics (LIPIcs), Volume 236, pp. 8:1-8:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2022)

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@InProceedings{nadel:LIPIcs.SAT.2022.8,
  author =	{Nadel, Alexander},
  title =	{{Introducing Intel(R) SAT Solver}},
  booktitle =	{25th International Conference on Theory and Applications of Satisfiability Testing (SAT 2022)},
  pages =	{8:1--8:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-242-6},
  ISSN =	{1868-8969},
  year =	{2022},
  volume =	{236},
  editor =	{Meel, Kuldeep S. and Strichman, Ofer},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.SAT.2022.8},
  URN =		{urn:nbn:de:0030-drops-166825},
  doi =		{10.4230/LIPIcs.SAT.2022.8},
  annote =	{Keywords: SAT, CDCL, MaxSAT}
}
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