- Volume 19 Issue 12
DOI QR Code
Analysis of Nonlinear CA Using CLT
CLT를 활용한 비선형 CA의 분석
- Received : 2015.05.27
- Accepted : 2015.07.06
- Published : 2015.12.31
Method for finding the attractors is the important object to investigate in the linear/additive CA because it is a primary interest in applications like pattern recognition, pattern classification, design of associative memory and query processing etc. But the research has been so far mostly concentrated around linear/additive CA and it is not enough to modelize the complex real life problem. So nonlinear CA is demanded to devise effective models of the problem and solutions around CA model. In this paper we introduce CLT as an upgraded version of RMT and provide the process for finding the attractors and nonreachable states effectively through the CLT.
CA;nonlinear CA;NBCA;CLT;attractor;nonreachable state
- John von Neumann, Theory of Self-Reproducing Automata, Arthur W. Burks ed. Univ. of Illinois Press, Urbana and London, 1966.
- M. Arbib, "Simple Self-reproducing universal automata," Information and Control, vol. 9, pp. 177-289, 1966. https://doi.org/10.1016/S0019-9958(66)90220-8
- E.R. Banks, "Information Processing and Transmission in Cellular Automata," Ph.D. thesis, MIT, 1971.
- S.J. Cho, U.S. Choi, H.D. Kim, Y.H. Hwang, J.G. Kim, S.H. Heo, "New Synthesis of One-Dimensional 90/150 Linear Hybrid Group Cellular Automata," Computer-Aided Design of Integrated Circuits and Systems, IEEE Trans. vol. 26, no. 9, pp. 1720-1724, 2007. https://doi.org/10.1109/TCAD.2007.895784
- O. Martin, A. M. Odlyzko, and Stephan Wolfram, "Algebraic Properties of Cellular Automata," Comm. Math. Phys. vol. 93, pp. 219-258, 1984. https://doi.org/10.1007/BF01223745
- S. Wolfram, "Statistical mechanics of cellular automata," Rev. Mod. Phys. 55(3), 601-644, 1983. https://doi.org/10.1103/RevModPhys.55.601
- S. Wolfram, "Random sequence generation by cellular automata," Advances in Applied Mathematics, vol. 7, no. 2, pp. 123-169, 1986. https://doi.org/10.1016/0196-8858(86)90028-X
- A. Wuensche and M. Lesser, The Global Dynamics of Cellular Automata; An Atlas of Basin of Attraction Fields of One-Dimensional Cellular Automata. Santa Fe Inst. Studies in the Sci. of Complexity, Addison Wesley, 1992.
- N. Ganguly, A. Das, P. Maji, B. K. Sikdar, and P. P. Chaudhuri, Evolution of cellular automata based associative memory for pattern recognition, High Performance Computing, Hyderabad, India, 2001.
- P. Pal Chaudhuri, D. Roy Choudhury, S. Nandi, and S. Chattopadhyay, Additive Cellular Automata Theory and Applications, vol. 1. IEEE Computer Society Press, USA, 1997.
- N. Ganguly, Cellular Automata Evolution : Theory and Applications in Pattern Recognition and Classification. Ph.D. thesis, Bengal Engineering College (a Deemed University), India, 2004.
- S.J. Cho, H.D. Kim, S.T. Kim, U.S. Choi, K.J. Lee, G.T. Kong, and J.G. Kim, "Finding Nonreachable State of a Linear TPMACA," submitted.
- Sukanta Das, Biplab K. Sikdar, and P. Pal Chaudhuri, "Characterization of Reachable/Nonreachable Cellular Automata States," ACRI 2004, LNCS 3305, pp. 813-822, 2004.
- Sukanta Das, Anirban Kundu, Biplab K. Sikdar, and P.Pal Chaudhuri, "Design of Nonlinear CA Based TPG Without Prohibited Pattern Set In Linear Time," Journal of Electronic testing: Theory and Applications, vol. 21, no. 1, pp. 95-107, 2005. https://doi.org/10.1007/s10836-005-5290-y
- Sukanta Das, Sukanya Mukherjee, and Nazma Naskar, and Biplab K. Sikdar, "Characterization of Single Cycle CA and its Application in Pattern Classification," Electronic Notes in Theoretical Computer Science, vol. 252, pp. 181-203, 2009. https://doi.org/10.1016/j.entcs.2009.09.021