Abstract
Motivated by applications in boolean-circuit design, boolean synthesis is the process of synthesizing a boolean function with multiple outputs, given a relation between its inputs and outputs. Previous work has attempted to solve boolean functional synthesis by converting a specification formula into a Binary Decision Diagram (BDD) and quantifying existentially the output variables. We make use of the fact that the specification is usually given in the form of a Conjunctive Normal Form (CNF) formula, and we can perform resolution on a symbolic representation of a CNF formula in the form of a Zero-suppressed Binary Decision Diagram (ZDD). We adapt the realizability test to the context of CNF and ZDD, and show that the Cross operation defined in earlier work can be used for witness construction. Experiments show that our approach is complementary to BDD-based Boolean synthesis.
Work supported in part by NSF grants CCF-1704883,IIS-1830549, CNS-2016656, DoD MURI grant N00014-20-1-2787, and an award from the Maryland Procurement Office.
Currently at Runtime Verification, Inc.
Chapter PDF
Similar content being viewed by others
Keywords
References
Akshay, S., Chakraborty, S., Goel, S., Kulal, S., Shah, S.: What’s hard about Boolean functional synthesis? In: Proc. 30th Int’l Conf. on Computer Aided Verification, Part I. Lecture Notes in Computer Science, vol. 10981, pp. 251–269. Springer (2018). https://doi.org/10.1007/978-3-319-96145-3_14
Bryant, R.: Graph-based algorithms for Boolean-function manipulation. IEEE Transactions on Computing C-35(8), 677–691 (1986)
Chakraborty, S., Fried, D., Tabajara, L.M., Vardi, M.Y.: Functional synthesis via input-output separation. In: Proc. 2018 IEEE Conf. on Formal Methods in Computer Aided Design. pp. 1–9. IEEE (2018). https://doi.org/10.23919/FMCAD.2018.8603000
Chatalic, P., Simon, L.: Multi-resolution on compressed sets of clauses. In: Proc 12th IEEE Int’l Conf. on Tools with Artificial Intelligence. pp. 2–10. IEEE Computer Society (2000). https://doi.org/10.1109/TAI.2000.889839
Chatalic, P., Simon, L.: ZRES: The old Davis-Putman procedure meets ZBDD. In: Proc. 17th Int’l Conf. on Automated Deduction. Lecture Notes in Computer Science, vol. 1831, pp. 449–454. Springer (2000)
Crama, Y., Hammer, P.L.: Boolean functions: Theory, algorithms, and applications. Cambridge University Press (2011)
Dechter, R., van Beek, P.: Local and global relational consistency. Theor. Comput. Sci. 173(1), 283–308 (1997)
Dudek, J.M., Phan, V.H.N., Vardi, M.Y.: Procount: Weighted projected model counting with graded project-join trees. In: Proc. 24th Int’l Conf. on Theory and Applications of Satisfiability Testing. Lecture Notes in Computer Science, vol. 12831, pp. 152–170. Springer (2021). https://doi.org/10.1007/978-3-030-80223-3_11
Fried, D., Tabajara, L.M., Vardi, M.Y.: BDD-based Boolean functional synthesis. In: Proc. 28th Int’l Conf. on Computer Aided Verification. Part II. Lecture Notes in Computer Science, vol. 9780, pp. 402–421. Springer (2016). https://doi.org/10.1007/978-3-319-41540-6_22
Golia, P., Roy, S., Meel, K.S.: Manthan: A data-driven approach for Boolean function synthesis. In: Proc. 32nd Int’l Conf. on on Computer Aided Verification, Part II. Lecture Notes in Computer Science, vol. 12225, pp. 611–633. Springer (2020). https://doi.org/10.1007/978-3-030-53291-8_31
Gomes, C.P., Selman, B.: Algorithm portfolio design: Theory vs. practice. arXiv preprint arXiv:1302.1541 (2013)
Hofferek, G., Gupta, A., Könighofer, B., Jiang, J.R., Bloem, R.: Synthesizing multiple Boolean functions using interpolation on a single proof. In: Proc. 2013 IEEE Conf. Formal Methods in Computer-Aided Design. pp. 77–84. IEEE (2013)
John, A.K., Shah, S., Chakraborty, S., Trivedi, A., Akshay, S.: Skolem functions for factored formulas. In: Proc. 2015 IEEE Conf. Formal Methods in Computer-Aided Design. pp. 73–80. IEEE (2015)
Knuth, D.E.: The Art of Computer Programming, Volume 4, Pre-Fascicle 1B: A Draft of Section 7.1.4: Binary Decision Diagrams. Addison-Wesley Professional, 12th edn. (2009)
Kukula, J.H., Shiple, T.R.: Building circuits from relations. In: Proc. 12th Int’l Conf. on Computer Aided Verification. Lecture Notes in Computer Science, vol. 1855, pp. 113–123. Springer (2000). https://doi.org/10.1007/10722167_12
Minato, S.: Zero-suppressed BDDs for set manipulation in combinatorial problems. In: Proc. 30th Design Automation Conference. pp. 272–277. ACM Press (1993). https://doi.org/10.1145/157485.164890
Mishchenko, A.: Introduction to zero-suppressed decision diagrams. Synthesis Lectures on Digital Circuits and Systems 45 (2001)
Narizzano, M., Pulina, L., Tacchella, A.: The QBFEVAL web portal. In: Proc. 10th European Conf. on Logics in Artificial Intelligence. Lecture Notes in Computer Science, vol. 4160, pp. 494–497. Springer (2006). https://doi.org/10.1007/11853886_45
Pan, G., Vardi, M.Y.: Symbolic decision procedures for QBF. In: Proc. 10th Int’l Conf. Principles and Practice of Constraint Programming. Lecture Notes in Computer Science, vol. 3258, pp. 453–467. Springer (2004). https://doi.org/10.1007/978-3-540-30201-8_34
Rabe, M.N., Seshia, S.A.: Incremental determinization. In: Proc. 19th Int’l Conf. on Theory and Applications of Satisfiability Testing. Lecture Notes in Computer Science, vol. 9710, pp. 375–392. Springer (2016). https://doi.org/10.1007/978-3-319-40970-2_23
Sasao, T., Butler, J.T.: Applications of zero-suppressed decision diagrams. Synthesis Lectures on Digital Circuits and Systems 9(2), 1–123 (2014)
Somenzi, F.: CUDD: CU Decision Diagram Package Release 3.0.0. University of Colorado at Boulder (2015)
Tabajara, L.M., Vardi, M.Y.: Factored Boolean functional synthesis. In: Proc. 2017 IEEE Conf. on Formal Methods in Computer Aided Design. pp. 124–131. IEEE (2017). https://doi.org/10.23919/FMCAD.2017.8102250
Zhu, S., Tabajara, L.M., Li, J., Pu, G., Vardi, M.Y.: Symbolic LTLf synthesis. In: Proc. 26th Int’l Joint Conf. on Artificial Intelligence. pp. 1362–1369. ijcai.org (2017)
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Open Access This chapter is licensed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license and indicate if changes were made.
The images or other third party material in this chapter are included in the chapter's Creative Commons license, unless indicated otherwise in a credit line to the material. If material is not included in the chapter's Creative Commons license and your intended use is not permitted by statutory regulation or exceeds the permitted use, you will need to obtain permission directly from the copyright holder.
Copyright information
© 2022 The Author(s)
About this paper
Cite this paper
Lin, Y., Tabajara, L.M., Vardi, M.Y. (2022). ZDD Boolean Synthesis. In: Fisman, D., Rosu, G. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2022. Lecture Notes in Computer Science, vol 13243. Springer, Cham. https://doi.org/10.1007/978-3-030-99524-9_4
Download citation
DOI: https://doi.org/10.1007/978-3-030-99524-9_4
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-030-99523-2
Online ISBN: 978-3-030-99524-9
eBook Packages: Computer ScienceComputer Science (R0)
