BLOCK TRANSFORMATION OF HYBRID CELLULAR AUTOMATA

Bo Chen; Fangyue Chen; Junbiao Guan; Genaro J. Martınez

doi:10.11948/2016077

2016 Volume 6 Issue 4

Article Contents

Article navigation > Journal of Applied Analysis & Computation > 2016 > 6(4): 1164-1179

Next Article Previous Article

Bo Chen, Fangyue Chen, Junbiao Guan, Genaro J. Martınez. BLOCK TRANSFORMATION OF HYBRID CELLULAR AUTOMATA[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1164-1179. doi: 10.11948/2016077

Citation:

Bo Chen, Fangyue Chen, Junbiao Guan, Genaro J. Martınez. BLOCK TRANSFORMATION OF HYBRID CELLULAR AUTOMATA[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 1164-1179. doi: 10.11948/2016077

BLOCK TRANSFORMATION OF HYBRID CELLULAR AUTOMATA

1 Department of Mathematics, School of Science, Hangzhou Dianzi University, Hangzhou, Zhejiang 310018, China;
2 Escuela Superior de Cómputo, Instituto Politécnico Nacional, México D. F., México;
3 International Center of Unconventional Computing, University of the West of England, BS16 1QY Bristol, United Kingdom

Fund Project:

Abstract

Abstract

By introducing a sequence-block transformation and vector-block transformation, we explore the dynamical properties of hybrid cellular automation (HCA) and hybrid cellular automation with memory (HCAM) in the framework of symbolic dynamics. As the local evolution rules of HCA and HCAM are not-uniform, the new uniform cellular automata (CAs) with multiple states are constructed by specifical the block transformations. Furthermore, because the new CA rules are topologically conjugate with the originals, the complex dynamics of the HCA and HCAM rules can be investigated via the new CA rules.
- Hybrid cellular automata /
- minority memory /
- block transform /
- symbolic dynamics /
- chaos
MSC: 37B10;37B15;65P20

FullText(HTML)

References

[1]	R. Alonso-Sanz, Elementary cellular automata with memory of delay type, 19th International Workshop, AUTOMATA 2013, 8155(2013), 67-83. Google Scholar
[2]	R. Alonso-Sanz and M. Martin, Elementary cellular automata with memory, Complex Systems, 14(2003)(2), 99-126. Google Scholar
[3]	R. Alonso-Sanz and M. Martin, Three-state one-dimensional cellular automata with memory, Chaos, Solitons and Fract., 21(2004)(4), 809-834. Google Scholar
[4]	J. Binghama and B. Binghamb, Hybrid one-dimensional reversible cellular automata are regular, Discrete Appl. Math., 155(2007)(18), 2555-2566. Google Scholar
[5]	K. Cattell and J. C. Muzio, Synthesis of one-dimensional linear hybrid cellular automata, IEEE Trans. Computers, 15(1996)(3), 325-335. Google Scholar
[6]	F. Y. Chen, W. F. Jin,G. R. Chen, F. F. Chen and L. Chen, Chaos of elementary cellular automata rule 42 of wolfram's class Ⅱ, Chaos, 19(2009)(1), 013140. Google Scholar
[7]	L. O. Chua and G. E. Pazienza, A nonlinear dynamics perspective of Wolfram's new kind of science. Part XⅡ:period-3, period-6, and permutive rules, Int. J. Bifur. Chaos, 19(2009)(12), 3887-4038. Google Scholar
[8]	L. O. Chua and G. E. Pazienza, A nonlinear dynamics perspective of Wolfram's new kind of science. Part XⅢ:Bernoulli σ_τ-shift rules, Int. J. Bifur. Chaos, 20(2010)(7), 1859-2003. Google Scholar
[9]	L. O. Chua, G. E. Pazienza and J. Shin, A nonlinear dynamics perspective of Wolfram's new kind of science. Part X:period-1 rules, Int. J. Bifur. Chaos, 19(2009)(5), 1425-1654. Google Scholar
[10]	L. O. Chua, G. E. Pazienza and J. Shin, A nonlinear dynamics perspective of Wolfram's new kind of science. Part XI:period-2 rules, Int. J. Bifur. Chaos, 19(2009)(6), 1751-1930. Google Scholar
[11]	L. O. Chua, V. I. Sbitnev and S. Yoon, A nonlinear dynamics perspective of Wolfram's new kind of science. Part I:threshold of complexity, Int. J. Bifur. Chaos, 12(2002)(12), 2655-2766. Google Scholar
[12]	M. Cook, Universality in elementary cellular automata, Complex Syst., 15(2004)(1), 1-40. Google Scholar
[13]	W. F. Jin, F. Y. Chen, G. R. Chen, L. Chen and F. F. Chen, Extending the symbolic dynamics of Chua's Bernoulli-shift rule 56, J. Cell. Automata, 5(2010)(1-2), 121-138. Google Scholar
[14]	B. Kitchens, Symbolic Dynamics:One-Sided, Two-Sided and Countable State Markov Shifts, Springer-Verlag, Berlin, 1998. Google Scholar
[15]	G. J. Martínez, A. Adamatzky and R. Alonso-Sanz, Designing complex dynamics in cellular automata with memory, Int. J. Bifur. Chaos, 23(2013)(10), 1330035. Google Scholar
[16]	G. J. Martínez, A. Adamatzky, R. Alonso-Sanz and J. C. Seck-Tuoh-Mora, Complex dynamic emerging in rule 30 with majority memory, Complex Systems, 18(2010)(3), 345-365. Google Scholar
[17]	G. J. Martínez, A. Andrew, F. Y. Chen and L. O. Chua, On Soliton Collisions Between Localizations in Complex ECA:Rules 54 and 110 and Beyond, Complex Syst., 21(2012)(2), 1-26. Google Scholar
[18]	G. J. Martínez, A. Andrew and H. V. McIntosh, Phenomenology of Glider Collisions in Cellular Automaton Rule 54 and Associated Logical Gates, Chaos, Solitons & Fract., 28(2006)(1), 100-111. Google Scholar
[19]	G. J. Martínez, A. Adamatzky, J. C. Seck-Tuoh-Mora and R. Alonso-Sanz, How to make dull cellular automata complex by adding memory:rule 126 case study, Complexity, 15(2010)(6), 34-49. Google Scholar
[20]	D. Radu, Hybrid cellular automata as pseudo-random number generators with binary synchronization property, in Proceedings of the International Symposium on Signals Circuits and Systems, 2009, 389-392. Google Scholar
[21]	C. F. Rubio, L. H. Encinas, S. H. White, A. M. Rey and G. R. Sánchez, The use of linear hybrid cellular automata as pseudorandom bit generators in cryptography, Neural Parallel Sci. Comput., 12(2004)(2), 175-192. Google Scholar
[22]	D. Radu and D. Ioana, Efficient and cryptographically secure pseudorandom number generators based on chains of hybrid cellular automata maps, in Proceedings of COMM 201410th International Conference on Communications, 2014. Google Scholar
[23]	J. von-Neumann, Theory of Self-reproducing Automata, University of Illinois Press, Urbana, 1966. Google Scholar
[24]	S. Wolfram, Statistical mechanics of cellular automata, Rev. Mod. Phys., 55(1983)(3), 601-644. Google Scholar
[25]	S. Wolfram, Universality and complexity in cellular automata, Phys. D, 10(1984)(1-2), 1-35. Google Scholar
[26]	S. Wolfram, Theory and Applications of Cellular Automata, World Scientifc, Singapore, 1986. Google Scholar
[27]	S. Wolfram, A New Kind of Science, Wolfram Media, Champaign, 2002. Google Scholar
[28]	Z. L. Zhou, Symbolic Dynamics, Shanghai Scientific and technological Education Publishing House, Shanghai, 1997. Google Scholar
[29]	Z. L. Zhou, Chaos and topological entropy, Acta Math. Sin., 31(1988)(1), 83-87. Google Scholar