AllSAT for Combinational Circuits

Dror Fried, Alexander Nadel, Yogev Shalmon

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review


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.

Original languageEnglish
Title of host publication26th International Conference on Theory and Applications of Satisfiability Testing, SAT 2023
EditorsMeena Mahajan, Friedrich Slivovsky
PublisherSchloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing
ISBN (Electronic)9783959772860
StatePublished - Aug 2023
Event26th International Conference on Theory and Applications of Satisfiability Testing, SAT 2023 - Alghero, Italy
Duration: 4 Jul 20238 Jul 2023

Publication series

NameLeibniz International Proceedings in Informatics, LIPIcs
ISSN (Print)1868-8969


Conference26th International Conference on Theory and Applications of Satisfiability Testing, SAT 2023

Bibliographical note

Funding Information:
Funding Yogev Shalmon: This research was partially supported by The Open University of Israel’s Research Fund (grant no. 41662).

Publisher Copyright:
© 2023 Schloss Dagstuhl- Leibniz-Zentrum fur Informatik GmbH, Dagstuhl Publishing. All rights reserved.


  • AllSAT
  • Circuits
  • SAT


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