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Boolean Network Models of Collective Dynamics of Open and Closed Large-Scale Multi-agent Systems

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Industrial Applications of Holonic and Multi-Agent Systems (HoloMAS 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10444))

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Abstract

This work discusses theoretical models of decentralized large-scale cyber-physical and other types of multi-agent systems (MAS). Arguably, various types of Boolean Networks are among the simplest such models enabling rigorous mathematical and computational analysis of the emerging behavior of such systems and their collective dynamics. This paper investigates determining possible asymptotic dynamics of several classes of Boolean Networks (BNs) such as Discrete Hopfield Networks, Sequential and Synchronous Dynamical Systems, and (finite, Boolean-valued) Cellular Automata. Viewing BNs as an abstraction for a broad variety of decentralized cyber-physical, computational, biological, social and socio-technical systems, similarities and differences between open and closed such systems are rigorously analyzed. Specifically, this paper addresses the problem of enumerating all possible dynamical evolutions of large-scale decentralized cyber-physical, cyber-secure and holonic systems abstracted as Boolean Networks. We establish that, in general, the problem of enumerating possible dynamics is provably computationally hard for both “open” and “closed” variants of BNs, even when all of the following restrictions simultaneously hold: (i) the local behaviors (node update rules) are very simple, monotone Boolean-valued functions; (ii) the network topology is sparse; and (iii) either there is no external environment impact on the system, or the model of the environment is of a rather simple, deterministic nature. Our results provide lower bounds on the complexity of possible behaviors of “real-world” large-scale cyber-physical, socio-technical, social and other distributed systems and infrastructures, with some far-reaching implications insofar as (un)predictability of such systems’ collective dynamics.

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References

  1. Bandini, S., Manzoni, S., Simone, C.: Heterogeneous agents situated in heterogeneous spaces. Appl. Artif. Intell. Int. J. 16(9–10), 831–852 (2002). Taylor & Francis

    Article  Google Scholar 

  2. Barrett, C., et al.: Gardens of Eden and fixed points in sequential dynamical systems. In: Discrete Mathematics & Theoretical Computer Science (DMTCS), vol. AA, pp. 95–110 (2001)

    Google Scholar 

  3. Barrett, C., et al.: Reachability problems for sequential dynamical systems with threshold functions. Theoret. Comput. Sci. 295(1–3), 41–64 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  4. Davey, N., Calcraft, L., Adams, R.: High capacity, small world associative memory models. Connect. Sci. 18(3), 247–264 (2006)

    Article  Google Scholar 

  5. Floreen, P., Orponen, P.: On the computational complexity of analyzing hopfield nets. Complex Syst. 3, 577–587 (1989)

    MathSciNet  MATH  Google Scholar 

  6. Graudenzi, A., et al.: Dynamical properties of a Boolean model of gene regulatory network with memory. J. Comput. Biol. 18(10), 1291–1303 (2011). https://doi.org/10.1089/cmb.2010.0069

    Article  MathSciNet  Google Scholar 

  7. Helbing, D.: Social Self-Organization. Understanding Complex Systems. Springer, Heidelberg (2012)

    Book  Google Scholar 

  8. Hopfield, J.: Neural networks and physical systems with emergent\collective computational abilities. Proc. Nat. Acad. Sci. 79, 2554–2558 (1982)

    Article  MathSciNet  Google Scholar 

  9. Hopfield, J., Tank, D.: Neural computation of decisions in optimization problems. Biol. Cybern. 52, 141–152 (1985)

    MATH  Google Scholar 

  10. Kauffman, S.A.: Emergent properties in random complex automata. Phys. D: Nonlin. Phenom. 10(1–2), 145–156 (1984)

    Article  MathSciNet  Google Scholar 

  11. Mortveit, H., Reidys, C.: Discrete sequential dynamical systems. Discrete Math. 226(1–3), 281–295 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  12. Orponen, P.: Computational complexity of neural networks: a survey. Nord. J. Comput. 1(1), 94–110 (1994)

    MathSciNet  Google Scholar 

  13. Sima, J., Orponen, P.: General-purpose computation with neural networks: a survey of complexity theoretic results. Neural Comput. 15(12), 2727–2778 (2003)

    Article  MATH  Google Scholar 

  14. Tošić, P.T., et al.: Modeling a system of UAVs on a mission, invited session on agent-based computing. In: Proceedings of 7th World Multiconference on Systemics, Cybernetics, and Informatics (SCI 2003), pp. 508–514 (2003)

    Google Scholar 

  15. Tošić, P.T., Agha, G.A.: On computational complexity of counting fixed points in symmetric Boolean graph automata. In: Calude, C.S., Dinneen, M.J., Păun, G., Pérez-Jímenez, M.J., Rozenberg, G. (eds.) UC 2005. LNCS, vol. 3699, pp. 191–205. Springer, Heidelberg (2005). doi:10.1007/11560319_18

    Chapter  Google Scholar 

  16. Tošić, P.T.: Cellular automata for distributed computing: models of agent interaction and their implications. In: Proceedings of International Conference Systems, Man & Cybernetics (SMC 2005), pp. 3204–3209. IEEE (2005)

    Google Scholar 

  17. Tošić, P.T.: On modeling and analyzing sparsely networked large-scale multi-agent systems with cellular and graph automata. In: Alexandrov, V.N., Albada, G.D., Sloot, P.M.A., Dongarra, J. (eds.) ICCS 2006. LNCS, vol. 3993, pp. 272–280. Springer, Heidelberg (2006). doi:10.1007/11758532_38

    Chapter  Google Scholar 

  18. Tošić, P.T.: On the complexity of counting fixed points and gardens of Eden in sequential & synchronous dynamical systems. Int. J. Found. Comput. Sci. (IJFCS) 17(5), 1179–1203 (2006). World Scientific

    Article  MATH  Google Scholar 

  19. Tošić, P.T.: Cellular automata communication models: comparative analysis of parallel, sequential and asynchronous ca with simple threshold update rules. Int. J. Nat. Comput. Res. (IJNCR) 1(3), 66–84 (2010)

    Article  Google Scholar 

  20. Tošić, P.T.: On the complexity of enumerating possible dynamics of sparsely connected Boolean network automata with simple update rules. In: Discete Mathematics and Theoretical Computer Science (DMTCS), pp. 125–144 (2010)

    Google Scholar 

  21. Tošić, P.T.: Modeling large-scale multi-agent systems with sequential and genuinely asynchronous cellular automata. Acta Phys. Pol. B (Proc. Suppl.) 4(2), 217–236 (2011). Polish Academy of Sciences

    Article  Google Scholar 

  22. Tošić, P.T.: On simple models of associative memory: network density is not required for provably complex behavior. In: Ascoli, G.A., Hawrylycz, M., Ali, H., Khazanchi, D., Shi, Y. (eds.) BIH 2016. LNCS, vol. 9919, pp. 61–71. Springer, Cham (2016). doi:10.1007/978-3-319-47103-7_7

    Chapter  Google Scholar 

  23. Tošić, P.T.: On phase transitions in dynamics of cellular and graph automata models of sparsely interconnected multi-agent systems. In: ACM Proceedings Autonomous Agents & Multi-agent Systems (AAMAS 2017), Sao Paulo, Brazil, May 2017

    Google Scholar 

  24. Tošić, P.T., Agha, G.: Understanding and modeling agent autonomy in dynamic multi-agent, multi-task environments. In: Proceedings of First European Workshop on Multi-Agent Systems (EUMAS 2003), Oxford, England, UK (2003)

    Google Scholar 

  25. Tošić, P.T., Ordonez, C.: Distributed protocols for multi-agent coalition formation: a negotiation perspective. In: Huang, R., Ghorbani, A.A., Pasi, G., Yamaguchi, T., Yen, N.Y., Jin, B. (eds.) AMT 2012. LNCS, vol. 7669, pp. 93–102. Springer, Heidelberg (2012). doi:10.1007/978-3-642-35236-2_10

    Chapter  Google Scholar 

  26. Garcia, J., Ordonez, C., Tošić, P.T.: Efficiently repairing and measuring replica consistency in distributed databases. Distr. Parallel Databases 31(3), 377–411 (2013)

    Article  Google Scholar 

  27. Vig, L., Adams, J.A.: Issues in multi-robot coalition formation. In: Parker, L.E., Schneider, F.E., Schultz, A.C. (eds.) Multi-Robot Systems: From Swarms to Intelligent Automata, vol. 3. Springer, Dordrecht (2005). doi:10.1007/1-4020-3389-3_2

    Google Scholar 

  28. Zhang, M.: Large-scale agent-based social simulation - a study on epidemic prediction and control. Ph.D. dissertation, TU Delft, The Netherlands (2016)

    Google Scholar 

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Authors and Affiliations

  1. Department of Computer Science, University of Idaho, Coeur D’Alene / Moscow, ID, USA

    Predrag T. Tošić

  2. Department of Computer Science, University of Houston, Houston, TX, USA

    Carlos Ordonez

Authors
  1. Predrag T. Tošić
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  2. Carlos Ordonez
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Correspondence to Predrag T. Tošić .

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Editors and Affiliations

  1. Czech Technical University, Prague, Czech Republic

    Vladimír Mařík

  2. German Research Center for AI, Saarbrücken, Germany

    Wolfgang Wahlster

  3. Austrian Institute of Technology, Vienna, Austria

    Thomas Strasser

  4. Czech Technical University, Prague, Czech Republic

    Petr Kadera

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Tošić, P.T., Ordonez, C. (2017). Boolean Network Models of Collective Dynamics of Open and Closed Large-Scale Multi-agent Systems. In: Mařík, V., Wahlster, W., Strasser, T., Kadera, P. (eds) Industrial Applications of Holonic and Multi-Agent Systems. HoloMAS 2017. Lecture Notes in Computer Science(), vol 10444. Springer, Cham. https://doi.org/10.1007/978-3-319-64635-0_8

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  • DOI: https://doi.org/10.1007/978-3-319-64635-0_8

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  • Print ISBN: 978-3-319-64634-3

  • Online ISBN: 978-3-319-64635-0

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