Abstract
Cellular Automata (CA) have long attracted interest as abstract computation models, but only in the last few years have serious attempts started to implement them in terms of molecules. Such nano-technological innovations promise very cost-effective fabrication because of the regular structure of CA, which allows assembly through molecular self-organization. The small sizes of molecules combined with their availability in Avogadro-scale numbers promises a huge computational power, in which the massive parallelism inherent in CA can be effectively exploited. This paper discusses the molecular CA in (Bandyopadhyay et al., Nature Physics 2010) and shows novel features that have never been proposed in conventional CA models. The interaction rules in the molecular CA are found to be of a mixed variety, ranging from conventional direct-neighborhood type of rules to rules with long-distance interactions between cells. The probabilities according to which rules are applied in the molecular CA are dynamically influenced by the patterns on the cellular space. This results in extremely rich behavior, as compared to conventional models, which has the potential to be utilized for efficient configuration of patterns on the cellular space.
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Density Functional Theory (DFT) is a quantum mechanical modeling method, which can be used to determine the properties of a many-electron system by using spatially dependent electron density.
References
Adachi S, Lee J, Peper F (2004) On signals in asynchronous cellular spaces. IEICE Trans Inform Syst E87-D(3):657–668
Adachi S, Peper F, Lee J (2004) Universality of hexagonal asynchronous totalistic Cellular Automata. In: Cellular Automata, Lecture Notes in Computer Science, vol 3305, pp 91–100
Adamatzky A, Teuscher C (eds) (2006) From utopian to genuine unconventional computers. Uniliver Press, Frome BA11 6TT UK
Bandyopadhyay A, Miki K, Wakayama Y (2006) Writing and erasing information in multilevel logic systems of a single molecule using scanning tunneling microscope (STM). Appl Phys Lett 89(24):243507–243507
Bandyopadhyay A, Acharya S (2008) A 16-bit parallel processing in a molecular assembly. Proc Natl Acad Sci USA 105(10):3668–3672
Bandyopadhyay A, Pati R, Sahu S, Peper F, Fujita D (2010) Massively parallel computing on an organic molecular layer. Nat Phys 6(5):369–375
Bandyopadhyay A, Pati R, Sahu S, Peper F, Fujita D (2010) Massively parallel computing on an organic molecular layer. Nat Phys, Supplementary Movie 4. http://www.nature.com/nphys/journal/v6/n5/extref/
Carter FL (1984) The molecular device computer: point of departure for large scale Cellular Automata. Phys D 10(1–2):175–194
Durbeck LJK, Macias NJ (2001) The cell matrix: an architecture for nanocomputing. Nanotechnology 12(3):217–230
Eigler DM, Lutz CP, Crommie MF, Manoharan HC, Heinrich AJ, Gupta JA (2004) Information transport and computation in nanometre-scale structures. Philos Trans R Soc Lond A 362(1819):1135–1147
Fredkin E, Toffoli T (1982) Conservative logic. Int J Theor Phys 21(3–4):219–253
Gaylord RJ, Nishidate K (1996) Modeling nature. Springer, Santa Clara
Heinrich AJ, Lutz CP, Gupta JA, Eigler DM (2002) Molecule cascades. Science 298(5597):1381–1387
Hjelmfelt A, Weinberger ED, Ross J (1991) Chemical implementation of neural networks and turing machines. Proc Natl Acad Sci USA 8:10983–10987
Higuchi T, Murakawa M, Iwata M, Kajitani I, Liu W, Salami M (1997) Evolvable hardware at function level. In: Proceedings of IEEE into conference on evolutionary computation (ICEC), pp 187–192
Imre A, Csaba G, Ji L, Orlov A, Bernstein GH, Porod W (2006) Majority logic gate for magnetic quantum-dot Cellular Automata. Science 311(5758):205–208
Isokawa T, Kowada S, Takada Y, Peper F, Kamiura N, Matsui N (2007) Defect-tolerance in cellular nanocomputers. New Gen Comput 25(2):171–199
Lent CS, Tougaw PS, Porod W, Bernstein GH (1993) Quantum Cellular Automata. Nanotechnology 4(1):49–57
Morita K, Margenstern M, Imai K (1998) Universality of reversible hexagonal Cellular Automata. MFCS’98 Satellite workshop on frontiers between decidability and undecidability. Brno, Czech Republic
Peper F, Lee J, Adachi S, Mashiko S (2003) Laying out circuits on asynchronous cellular arrays: a step towards feasible nanocomputers? Nanotechnology 14(4):469–485
Peper F, Bandyopadhyay A, Oono H, Sahu S, Pati R, Ghosh S, Isokawa T, Fujita D (2010) On molecular implementations of Cellular Automata. In: Proceedings of the 10th international conference on applied computer science (ACS’10), pp 401–405
Sahu S, Oono H, Ghosh S, Bandyopadhyay A, Fujita D, Peper F, Isokawa T, Pati R (2010) Molecular implementations of Cellular Automata. In: Proceedings of the 9th international conference on Cellular Automata for research and industry(ACRI’10), Lecture Notes in Computer Science, vol 6350, pp 650–659
Toffoli T (1984) CAM: A high-performance cellular automaton machine. Phys D 10(1–2):195–205
Acknowledgements
Authors acknowledge JSPS Grants in Aid for Young Scientists (A) for 2009-2011, Grant number 21681015 (Govt. of Japan). R.P. acknowledges National Science Foundation (NSF) Award number ECCS-0643420.
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Sahu, S., Oono, H., Ghosh, S. et al. On Cellular Automata rules of molecular arrays. Nat Comput 11, 311–321 (2012). https://doi.org/10.1007/s11047-012-9314-0
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DOI: https://doi.org/10.1007/s11047-012-9314-0