Abstract
The problem of generating r-contiguous detectors in negative selection can be transformed in the problem of finding assignment sets for a Boolean formula in k-CNF. Knowing this crucial fact enables us to explore the computational complexity and the feasibility of finding detectors with respect to the number of self bit strings \(|\mathcal{S}|\), the bit string length l and matching length r. It turns out that finding detectors is hardest in the phase transition region, which is characterized by certain combinations of parameters \(|\mathcal{S}|,l\) and r. This insight is derived by investigating the r-contiguous matching probability in a random search approach and by using the equivalent k-CNF problem formulation.
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References
Percus, J.K., Percus, O.E., Perelson, A.S.: Predicting the size of the T-cell receptor and antibody combining region from consideration of efficient self-nonself discrimination. Proceedings of National Academy of Sciences USA 90, 1691–1695 (1993)
D’haeseleer, P., Forrest, S., Helman, P.: An immunological approach to change detection: algorithms, analysis, and implications. In: Proceedings of the Symposium on Research in Security and Privacy, pp. 110–119. IEEE Computer Society Press, Los Alamitos (1996)
Forrest, S., Perelson, A.S., Allen, L., Cherukuri, R.: Self-nonself discrimination in a computer. In: Proceedings of the Symposium on Research in Security and Privacy, pp. 202–212. IEEE Computer Society Press, Los Alamitos (1994)
Ayara, M., Timmis, J., de Lemos, R., de Castro, L.N., Duncan, R.: Negative selection: How to generate detectors. In: ICARIS 2002. Proceedings of the 1nd International Conference on Artificial Immune Systems, pp. 89–98. University of Kent at Canterbury Printing Unit (2002)
Stibor, T., Timmis, J., Eckert, C.: On the appropriateness of negative selection defined over hamming shape-space as a network intrusion detection system. In: CEC 2005. Proceedings of Congress On Evolutionary Computation, pp. 995–1002. IEEE Press, New York (2005)
Stibor, T., Timmis, J., Eckert, C.: The link between r-contiguous detectors and k-CNF satisfiability. In: CEC 2006. Proceedings of Congress On Evolutionary Computation, pp. 491–498. IEEE Press, New York (2006)
Feller, W.: An Introduction to Probability Theory and its Applications, 3rd edn., vol. 1. John Wiley & Sons, West Sussex, England (1968)
Ranang, M.T.: An artificial immune system approach to preserving security in computer networks. Master’s thesis, Norges Teknisk-Naturvitenskapelige Universitet (2002)
Uspensky, J.V.: Introduction to Mathematical Probability. McGraw-Hill, New York (1937)
Freitas, A.A., Timmis, J.: Revisiting the foundations of artificial immune systems: A problem-oriented perspective. In: Timmis, J., Bentley, P.J., Hart, E. (eds.) ICARIS 2003. LNCS, vol. 2787, pp. 229–241. Springer, Heidelberg (2003)
González, F., Dasgupta, D., Gómez, J.: The effect of binary matching rules in negative selection. In: Cantú-Paz, E., Foster, J.A., Deb, K., Davis, L., Roy, R., O’Reilly, U.-M., Beyer, H.-G., Kendall, G., Wilson, S.W., Harman, M., Wegener, J., Dasgupta, D., Potter, M.A., Schultz, A., Dowsland, K.A., Jonoska, N., Miller, J., Standish, R.K. (eds.) GECCO 2003. LNCS, vol. 2723, pp. 195–206. Springer, Heidelberg (2003)
Stibor, T., Timmis, J., Eckert, C.: Generalization regions in hamming negative selection. In: Intelligent Information Processing and Web Mining. Advances in Soft Computing, pp. 447–456. Springer, Heidelberg (2006)
Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: Introduction to Algorithms, 2nd edn. MIT Press, Cambridge, MA (2002)
Kullmann, O.: The SAT, solver competition on random instances. Journal on Satisfiability, Boolean Modeling and Computation 2, 61–102 (2006)
Freeman, J.W.: Hard random 3-SAT problems and the Davis-Putnam procedure. Artificial Intelligence 81(1-2), 183–198 (1996)
Ouyang, M.: How good are branching rules in DPLL. Discrete Applied Mathematics 89(1-3), 281–286 (1998)
Davis, M., Logemann, G., Loveland, D.: A machine program for theorem-proving. Communications of the ACM 5(7), 394–397 (1962)
Davis, M., Putnam, H.: A computing procedure for quantification theory. Journal of the ACM (JACM) 7(3), 201–215 (1960)
Gent, I.P., Walsh, T.: The SAT phase transition. In: Proceedings of the 11th European Conference on Artificial Intelligence, pp. 105–109. John Wiley & Sons, West Sussex, England (1994)
Selman, B., Mitchell, D.G., Levesque, H.J.: Generating hard satisfiability problems. Artificial Intelligence 81(1-2), 17–29 (1996)
Achlioptas, D., Naor, A., Peres, Y.: Rigorous location of phase transitions in hard optimization problems. Nature 435, 759–764 (2005)
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Stibor, T. (2007). Phase Transition and the Computational Complexity of Generating r-Contiguous Detectors. In: de Castro, L.N., Von Zuben, F.J., Knidel, H. (eds) Artificial Immune Systems. ICARIS 2007. Lecture Notes in Computer Science, vol 4628. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-73922-7_13
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DOI: https://doi.org/10.1007/978-3-540-73922-7_13
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