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MDDs Boost Equation Solving on Discrete Dynamical Systems

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Integration of Constraint Programming, Artificial Intelligence, and Operations Research (CPAIOR 2021)

Abstract

Discrete dynamical systems (DDS) are a model to represent complex phenomena appearing in many different domains. In the finite case, they can be identified with a particular class of graphs called dynamics graphs. In [9] polynomial equations over dynamics graphs have been introduced. A polynomial equation represents a hypothesis on the fine structure of the system. Finding the solutions of such equations validate or invalidate the hypothesis.

This paper proposes new algorithms that enumerate all the solutions of polynomial equations with constant right-hand term outperforming the current state-of-art methods [10]. The boost in performance of our algorithms comes essentially from a clever usage of Multi-valued decision diagrams.

These results are an important step forward in the analysis of complex dynamics graphs as those appearing, for instance, in biological regulatory networks or in systems biology.

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References

  1. Akers, S.B.: Binary decision diagrams. IEEE Trans. Comput. 27(06) ,509–516 (1978)

    Google Scholar 

  2. Amilhastre, J., Fargier, H., Niveau, A., Pralet, C.: Compiling CSPs: a complexity map of (non-deterministic) multivalued decision diagrams. Int. J. Artif. Intell. Tools 23(04), 1460015 (2014)

    Article  Google Scholar 

  3. Andersen, H.R.: An introduction to binary decision diagrams. Lecture notes, available online, IT University of Copenhagen, p. 5 (1997)

    Google Scholar 

  4. Bergman, D., Cire, A.A., van Hoeve, W.: MDD propagation for sequence constraints. J. Artif. Intell. Res. 50, 697–722 (2014)

    Article  MathSciNet  Google Scholar 

  5. Bergman, D., Cire, A.A., Van Hoeve, W.J., Hooker, J.: Decision diagrams for optimization, vol. 1. Springer, Berlin (2016). https://doi.org/10.1007/978-3-319-42849-9

  6. Berndt, R., Bazan, P., Hielscher, K.S., German, R., Lukasiewycz, M.: Multi-valued decision diagrams for the verification of consistency in automotive product data. In: 2012 12th International Conference on Quality Software, pp. 189–192. IEEE (2012)

    Google Scholar 

  7. Cheng, K.C., Yap, R.H.: An MDD-based generalized arc consistency algorithm for positive and negative table constraints and some global constraints. Constraints 15(2), 265–304 (2010)

    Article  MathSciNet  Google Scholar 

  8. Darwiche, A., Marquis, P.: A knowledge compilation map. J. Artif. Intell. Res. 17, 229–264 (2002)

    Article  MathSciNet  Google Scholar 

  9. Dennunzio, A., Dorigatti, V., Formenti, E., Manzoni, L., Porreca, A.E.: Polynomial equations over finite, discrete-time dynamical systems. In: Mauri, G., El Yacoubi, S., Dennunzio, A., Nishinari, K., Manzoni, L. (eds.) ACRI 2018. LNCS, vol. 11115, pp. 298–306. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-99813-8_27

    Chapter  Google Scholar 

  10. Dennunzio, A., Formenti, E., Margara, L., Montmirail, V., Riva, S.: Solving equations on discrete dynamical systems. In: Cazzaniga, P., Besozzi, D., Merelli, I., Manzoni, L. (eds.) Computational Intelligence Methods for Bioinformatics and Biostatistics, pp. 119–132. Springer International Publishing, Cham (2020)

    Chapter  Google Scholar 

  11. Martello, S., Toth, P.: Knapsack Problems: Algorithms and Computer Implementations. Wiley, New York, NY, USA (1990)

    MATH  Google Scholar 

  12. Nakahara, H., Jinguji, A., Sato, S., Sasao, T.: A random forest using a multi-valued decision diagram on an FPGA. In: 2017 IEEE 47th International Symposium on Multiple-Valued Logic (ISMVL), pp. 266–271. IEEE (2017)

    Google Scholar 

  13. Naldi, A., Thieffry, D., Chaouiya, C.: Decision diagrams for the representation and analysis of logical models of genetic networks. In: Calder, M., Gilmore, S. (eds.) CMSB 2007. LNCS, vol. 4695, pp. 233–247. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-75140-3_16

    Chapter  Google Scholar 

  14. Perez, G., Régin, J.C.: Efficient operations on MDDs for building constraint programming models. In: IJCAI (2015)

    Google Scholar 

  15. Zaitseva, E., Levashenko, V., Kostolny, J., Kvassay, M.: A multi-valued decision diagram for estimation of multi-state system. In: Eurocon 2013, pp. 645–650. IEEE (2013)

    Google Scholar 

  16. Zhang, L., Xing, L., Liu, A., Mao, K.: Multivalued decision diagrams-based trust level analysis for social networks. IEEE Access 7, 180620–180629 (2019)

    Article  Google Scholar 

Download references

Acknowledgments

This work has been supported by the French government, through the 3IA Côte d’Azur Investments in the Future project managed by the National Research Agency (ANR) with the reference number ANR-19-P3IA-0002.

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Correspondence to Sara Riva .

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Formenti, E., Régin, JC., Riva, S. (2021). MDDs Boost Equation Solving on Discrete Dynamical Systems. In: Stuckey, P.J. (eds) Integration of Constraint Programming, Artificial Intelligence, and Operations Research. CPAIOR 2021. Lecture Notes in Computer Science(), vol 12735. Springer, Cham. https://doi.org/10.1007/978-3-030-78230-6_13

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  • DOI: https://doi.org/10.1007/978-3-030-78230-6_13

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