Abstract
Dualization of Boolean functions is a fundamental problem that appears in various fields such as artificial intelligence, logic, data mining, etc. For monotone Boolean functions, many empirical researches that focus on practical efficiency have recently been done. We extend our previous work for monotone dualization and present a novel method for dualization that allows us to handle any Boolean function, including non-monotone Boolean functions. We furthermore present a variant of this method in cooperation with all solutions solver. By experiments we evaluate efficiency and characteristics of our methods.
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Ausiello, G., Franciosa, P., Frigioni, D.: Directed hypergraphs: problems, algorithmic results, and a novel decremental approach. In: Proceedings of 14Th Italian Conference on Theoretical Computer Science (ICTCS 2001), pp.312–328. Torino, Italy (2001)
Bryant, R.: Graph-based algorithms for Boolean function manipulation. IEEE Trans. Comput. 35, 677–691 (1986)
Chen, H., Marques-Silva, J.: Tg-pro - a sat-based atpg system. http://logos.ucd.ie/web/doku.php?id=tg-pro Accessed on 16 May (2014)
clasp:a conflict-driven nogood learning answer set solver. http://www.cs.uni-potsdam.de/clasp/. Accessed on 4th August (2015)
Coudert, O., Madre, J.C.: Implicit and incremental computation of primes and essential primes of Boolean functions. In: Design Automation Conference, 1992. Proceedings., 29Th ACM/IEEE, pp. 36–39 (1992)
Crama, Y., Hammer, P.: Boolean Functions: Theory, Algorithms, and Applications. Encyclopedia of Mathematics and its Applications. Cambridge University Press (2011)
DB-TDD: Dualization of boolean functions using ternary decision diagrams. http://www.sd.is.uec.ac.jp/toda/code/dbtdd.html Accessed on 4th August (2015)
Eiter, T., Makino, K., Gottlob, G.: Computational aspects of monotone dualization: a brief survey. Discret. Appl. Math. 156, 2035–2049 (2008)
Gallo, G., Longo, G., Pallottino, S., Nguyen, S.: Directed hypergraphs and applications. Discret. Appl. Math. 42(2-3), 177–201 (1993)
Gebser, M., Kaufmann, B., Neumann, A., Schaub, T.: Conflict-driven answer set enumeration. In: Baral, C., Brewka, G., Schlipf, J. (eds.) Logic Programming and Nonmonotonic Reasoning, Lecture Notes in Computer Science, vol. 4483, pp. 136–148. Springer, Berlin Heidelberg (2007), doi:10.1007/978-3-540-72200-7_13
Knuth, D.: The Art of Computer Programming Volume 4a. Addison-Wesley Professional, New Jersey, USA (2011)
Minato, S.: Zero-Suppressed BDDs for Set Manipulation in Combinatorial Problems. In: 30Th ACM/IEEE Design Automation Conference(DAC-93), pp. 272–277. Dallas, Texas, USA (1993)
Minato, S.: Binary decision diagrams and applications for VLSI CAD kluwer academic publishers (1996)
Minato, S.I.: Zero-suppressed bdds and their applications. Int. J. Softw. Tools Technol. Transfer 3(2), 156–170. doi:10.1007/s100090100038
MINCE a new static global variable ordering for SAT & BDDs. http://www.aloul.net/Tools/mince/. Accessed on 16 May, 2014
Murakami, K., Uno, T.: Hypergraph dualization repository. http://research.nii.ac.jp/~uno/dualization.html Accessed on 19 January (2013)
Murakami, K., Uno, T.: Efficient algorithms for dualizing large-scale hypergraphs. In: Proceedings of the Meeting on Algorithm Engineering & Experiments (ALENEX), pp. 1–13. New Orleans, Louisiana, USA (2013)
Sasao, T.: Ternary decision diagrams survey. In: Proceedings of IEEE 27Th International Symposium on Multiple-Valued Logic (ISMVL ’97), pp. 241–250 (1997)
SATLIB - benchmark problems. http://www.cs.ubc.ca/~hoos/SATLIB/benchm.html. Accessed on 16 May, 2014
Shi, C.J., Brzozowski, J.A.: A characterization of signed hypergraphs and its applications to VLSI via minimization and logic synthesis. Discret. Appl. Math. 90 (1-3), 223–243 (1999)
Simha, R., Tripathi, R., Thakur, M.: Mining associations using directed hypergraphs Proceedings of the 2012 IEEE 28Th International Conference on Data Engineering Workshops (ICDEW ’12), pp. 190–197. IEEE Computer Society, Washington, DC, USA (2012)
Thurley, M.: The sharpsat #sat solver. https://sites.google.com/site/marcthurley/sharpsat Accessed on 16 May (2014)
Thurley, M.: Sharpsat counting models with advanced component caching and implicit bcp. In: Biere, A., Gomes, C. (eds.) Theory and Applications of Satisfiability Testing - SAT 2006, Lecture Notes in Computer Science, vol. 4121, pp. 424–429. Springer, Berlin Heidelberg (2006), doi:10.1007/11814948_38
Toda, T.: Fast Compression of Large-Scale Hypergraphs for Solving Combinatorial Problems. In: Proceedings of Sixteenth International Conference on Discovery Science (DS 2013), pp. 281–293. Singapore (2013)
Toda, T.: Hypergraph Transversal Computation with Binary Decision Diagrams. In: Proceedings of 11Th International Symposium on Experimental Algorithms (SEA 2013), pp. 91–102 (2013)
Toda, T., Tsuda, K.: Bdd construction for all solutions sat and efficient caching mechanism. In: Proceedings of the 30th Annual ACM Symposium on Applied Computing, SAC ’15, pp. 1880–1886. ACM, New York, NY, USA (2015), doi:10.1145/2695664.2695941
Wegener, I.: Branching Programs and Binary Decision Diagrams. Society for Industrial and Applied Mathematics. doi:10.1137/1.9780898719789 (2000)
Yasuoka, K.: A new method to represent sets of products: ternary decision diagrams. IEICE Trans. Fundam. Electron. Commun. Comput. Sci. E78-A, 1722–1728 (1995)
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This work was supported by JSPS KAKENHI Grant Number 26870011.
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Toda, T. Dualization of boolean functions using ternary decision diagrams. Ann Math Artif Intell 79, 229–244 (2017). https://doi.org/10.1007/s10472-016-9520-z
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DOI: https://doi.org/10.1007/s10472-016-9520-z