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On Improving the Expressive Power of Chemical Computation

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Part of the book series: Emergence, Complexity and Computation ((ECC,volume 22))

Abstract

The term chemical computation describes information processing setups where an arbitrary reaction system is used to perform information processing. The reaction system consists of a set of reactants and a reaction volume that harbours all chemicals. It has been argued that this type of computation is in principle Turing complete: for any computable function a suitable chemical system can be constructed that implements it. Turing completeness cannot be strictly guaranteed due to the inherent stochasticity of chemical reaction dynamics. The computation process can end prematurely or branch off in the wrong direction. The frequency of such errors defines the so-called fail rate of chemical computation. In this chapter we review recent advances in the field, and also suggest a few novel generic design principles which, when adhered to, should enable engineers to build accurate chemical computers.

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Notes

  1. 1.

    The results for d \(=\) 2,3 only qualitative since the results are not fully converged with respect to the size of the lattice. This analysis is illustrated briefly in Fig. 26.18.

  2. 2.

    We believe that the \(f_2\) values for \(d=2\) and \(d=3\) should be actually a bit higher due to lack of convergence for two \((d = 2)\) and three \((d = 3)\) dimensions with respect to the number of sites (cells) in the lattice.

  3. 3.

    The same problem with few successful while-loops arises. The specified numbers are for \(v_0=1\).

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Acknowledgments

This work has been supported by Chalmers University of Technology. A part of the work has been done for meeting the master’s degree requirements at Chalmers University of Technology.

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  1. Department of Microtechnology and Nanoscience - MC2, Chalmers University of Technology, SE-412, Göteborg, Sweden

    Erik Bergh & Zoran Konkoli

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  1. Erik Bergh
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  2. Zoran Konkoli
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Correspondence to Zoran Konkoli .

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  1. Unconventional Computing Centre, University of the West of England Unconventional Computing Centre, Bristol, United Kingdom

    Andrew Adamatzky

Appendix: Convergence Tests

Appendix: Convergence Tests

We studied how the number of lattice sites affects the simulation data. Extensive convergence tests were performed which consisted of analyzing how the graphs presented in this section change when the number of lattice sites is increased. A few examples are shown in Fig. 26.18.

The conclusions are as follows. For one \((d = 1)\) the convergence has been achieved and these results are quantitative. The results for two \((d = 2)\) dimensions are only qualitative. To obtain better results, the lattice size should be increased. This could not be done due to the usual hardware limitations. In these types of simulations the CPU speed is the most limiting factor.

Fig. 26.18
figure 18

Convergence tests of the fail rate versus number of nodes. The system is a minimal while loop implementation with \(k_1/k_2=10^6\) and \(v_0=1\). On the x-axis is the length in nodes of the domain. In panel a is the convergence test for one dimension, this yields that the x-axis also correspond to the total number of nodes. Panel b corresponds to two dimensions with the total number of nodes then being the x-axis value squared. Panel c consequently corresponds to three dimensions. Since the domain used has been \(5\times 5\times 4\) for three dimensions, the total number of nodes is the x-axis value cubed times a factor \(0.8\) due to the non-symmetry

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Bergh, E., Konkoli, Z. (2017). On Improving the Expressive Power of Chemical Computation. In: Adamatzky, A. (eds) Advances in Unconventional Computing. Emergence, Complexity and Computation, vol 22. Springer, Cham. https://doi.org/10.1007/978-3-319-33924-5_26

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  • DOI: https://doi.org/10.1007/978-3-319-33924-5_26

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