Abstract
In this paper, we present the results on describing and modeling dynamical properties of collective systems. In particular, we consider the problems of activation and deactivation of collectives, represented by networks, by establishing special agents called activators and deactivators in a network. Such problems are combinatorial and to solve them, we employ the algorithms for solving Boolean satisfiability problem (SAT). Thus, we describe the general technique for reducing the problems from a considered class to SAT. The paper presents the novel approach to analysis of problems related to Computer Security. In particular, we propose to study the developing and blocking of attacks on computer networks as the processes of activation/deactivation. We give a number of theoretical properties of corresponding discrete dynamical systems. For the problems of blocking attacks on computer networks, the corresponding reduction to SAT was implemented and tested. At the present moment using state-of-the-art SAT solvers, it is possible to solve such problems for networks with 200 vertices.
This is a preview of subscription content, log in via an institution to check access.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barabasi, A.L., Albert, R.: Emergence of scaling in random networks. Science 286(5439), 509–512 (1999)
Watts, D., Strogatz, S.: Collective dynamics of ’small-world’ networks. Nature 393(6684), 440–442 (1998)
Evdokimov, A.A., Kochemazov, S.E., Otpushchennikov, I.V., Semenov, A.A.: Study of discrete automaton models of gene networks of nonregular structure using symbolic calculations. J. Appl. Ind. Math. 8(3), 307–316 (2014)
Kochemazov, S., Semenov, A.: Using synchronous boolean networks to model several phenomena of collective behavior. PLOS ONE 9(12), 1–28 (2014)
Biere, A., Heule, M.J.H., van Maaren, H., Walsh, T.: Handbook of Satisfiability, Frontiers in Artificial Intelligence and Applications, vol. 185, Feb 2009. IOS Press
Dubrova, E., Teslenko, M.: A SAT-based algorithm for finding attractors in synchronous boolean networks. IEEE/ACM Trans. Comput. Biol. Bioinform. 8(5), 1393–1399 (2011)
Kauffman, S.: Metabolic stability and epigenesis in randomly constructed genetic nets. J. Theor. Biol. 22(3), 437–467 (1969)
Shannon, C.E.: A symbolic analysis of relay and switching circuits. Electr. Eng. 57(12), 713–723 (1938)
Cook, S.A.: The complexity of theorem proving procedures. In: Proceedings of the Third Annual ACM Symposium, pp. 151–158. ACM, New York (1971)
Levin, L.: Universal sequential search problems. Probl. Inf. Transm. 9(3), 265–266 (1973)
Tseitin, G.: On the complexity of derivation in propositional calculus. Studies in constructive mathematics and mathematical logic, part II, Seminars in mathematics, pp. 115–125 (1970)
Granovetter, M.: Threshold models of collective behavior. Am. J. Sociol. 83(6), 1420–1443 (1978)
Breer, V.V.: Game-theoretic models of collective conformity behavior. Autom. Remote Control 73(10), 1680–1692 (2012)
Erdös, P., Rényi, A.: On random graphs. Publications Mathematicae 6, 290–297 (1959)
Kochemazov, S., Semenov, A., Zaikin, O.: The application of parameterized algorithms for solving SAT to the study of several discrete models of collective behavior. In: 39th International Convention on Information and Communication Technology, Electronics and Microelectronics, MIPRO 2016, Opatija, Croatia, May 30–June 3, 2016, pp. 1288–1292. IEEE (2016)
Kochemazov, S., Zaikin, O., Semenov, A.: Improving the effectiveness of SAT approach in application to analysis of several discrete models of collective behavior. In: 40th International Convention on Information and Communication Technology, Electronics and Microelectronics, MIPRO 2017, Opatija, Croatia, May 22–26, 2017, pp. 1172–1177. IEEE (2017)
Danforth, M.: Models for threat assessment in networks. California Univ. Davis Dept. of Computer Science, Technical report (2006)
Ammann, P., Wijesekera, D., Kaushik, S.: Scalable, graph-based network vulnerability analysis. In: Proceedings of the 9th ACM Conference on Computer and Communications Security, pp. 217–224. CCS ’02. ACM, New York, NY, USA (2002)
Jha, S., Sheyner, O., Wing, J.M.: Two formal analysis of attack graphs. In: 15th IEEE Computer Security Foundations Workshop (CSFW-15 2002), 24–26 June 2002, Cape Breton, Nova Scotia, Canada, pp. 49–63 (2002)
Sheyner, O., Haines, J.W., Jha, S., Lippmann, R., Wing, J.M.: Automated generation and analysis of attack graphs. In: 2002 IEEE Symposium on Security and Privacy, Berkeley, California, USA, May 12–15, 2002, pp. 273–284 (2002)
Asin, R., Nieuwenhuis, R., Oliveras, A., Rodriguez-Carbonell, E.: Cardinality networks: a theoretical and empirical study. Constraints 16(2), 195–221 (2011)
Acknowledgements
The research was funded by Russian Science Foundation (project No. 16-11-10046).
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2018 Springer International Publishing AG, part of Springer Nature
About this paper
Cite this paper
Semenov, A., Gorbatenko, D., Kochemazov, S. (2018). Computational Study of Activation Dynamics on Networks of Arbitrary Structure. In: Kalyagin, V., Pardalos, P., Prokopyev, O., Utkina, I. (eds) Computational Aspects and Applications in Large-Scale Networks. NET 2016. Springer Proceedings in Mathematics & Statistics, vol 247. Springer, Cham. https://doi.org/10.1007/978-3-319-96247-4_15
Download citation
DOI: https://doi.org/10.1007/978-3-319-96247-4_15
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-96246-7
Online ISBN: 978-3-319-96247-4
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)