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AllSAT for Combinational Circuits

Authors Dror Fried, Alexander Nadel , Yogev Shalmon

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ACM Subject Classification
  • Mathematics of computing → Solvers
Keywords
  • AllSAT
  • SAT
  • Circuits

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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 Get BibTex

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) https://doi.org/10.4230/LIPIcs.SAT.2023.9

Author Details

Dror Fried
  • Department of Mathematics and Computer Science, The Open University of Israel, Ra’anana, Israel
Alexander Nadel
  • Intel Corporation, Haifa, Israel
  • Faculty of Data and Decision Sciences, Technion, Haifa, Israel
Yogev Shalmon
  • Intel Corporation, Haifa, Israel
  • The Open University of Israel, Ra’anana, Israel

Funding

  • Shalmon, Yogev: This research was partially supported by The Open University of Israel's Research Fund (grant no. 41662).

Acknowledgements

We are grateful to Supratik Chakraborty, Alexander Ivrii, Kuldeep Meel, Roberto Sebastiani, Mate Soos and Moshe Vardi for helpful discussions which played an important role in shaping our research. Also, we thank the anonymous reviewers for their comments and useful suggestions.

Supplementary Materials

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