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Programmable and parallel water computing

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Abstract

We further the work on a recently proposed membrane computing model which utilises decentralised water tanks interconnected by pipes with water flow controlled by valves. Although the system was shown to be universal, the system is complex and does not map to practical devices easily. We demonstrate that these water computing systems can ‘efficiently’ construct: (1) A programmable sequential, random-access machine (RAM), (2) a programmable exclusive read exclusive write (EREW) parallel random-access machine (PRAM). The resulting RAM and PRAM model presented in this paper is able to run different programs one after the other, with only needing to change the initial volume stored in the input tanks.

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Authors and Affiliations

  1. School of Computer Science, University of Auckland, Auckland, New Zealand

    Alec Henderson, Radu Nicolescu & Michael J. Dinneen

  2. Compucon New Zealand, Auckland, New Zealand

    TN Chan

  3. Department of Bioinformatics, Friedrich Schiller University of Jena, Jena, Germany

    Hendrik Happe & Thomas Hinze

Authors
  1. Alec Henderson
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  2. Radu Nicolescu
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  3. Michael J. Dinneen
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  4. TN Chan
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  5. Hendrik Happe
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Appendix A High level view of execution of RAM steps

Appendix A High level view of execution of RAM steps

Here we present a high level view of the evaluation of the RAM. Due to the size of implementing a real algorithm (the euclidean algorithm presented earlier would contain over 70 inputs) we show at a high level the evaluation of the separate parts (Fig. 21, 22, 23, 24, 25, 26, 27, 28, 29, 30, 31, 32, 33, 34, 35, 36, 37, 38, 39, 40).

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Step 1: Outer loop initial state the inputs are all full

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Step 2: The inputs are placed in the repeatable fetch to be passed to the operation

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Step 3: The operation will be executed as its inputs are full. Note the values are still kept in the repeatable fetch

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Step 4: The operation has completed. Note now the outer program will either go to step 5(i) if the program will end or step 5(ii) if it will run the next line

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Step 5(i) the process to fill the output control is started

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Step 6(i)

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Step 7(i)

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Step 8(i): The program has now ended

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Step 5(ii) The program will now cause the L tank to take the value from the s tank to loop again

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Step 6(ii)

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Step 7(ii) The program is ready to run line L

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Step 1: The inputs are full to select the operation

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Step 2: The operations inputs are filled/

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Step 3: The results are returned (available for the outer loop)

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Step 1: The first step of the increment operator. All of the inputs are filled

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Step 2: The operation has written to the register

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Step 3: The increment operator has now completed and the result is placed in the output tank

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Step 4: \(q_{1}'\) is filled. This tank ensures a synchronising step with both the write and increment needing to be completed

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Step 5: The write and increments output controls are drained

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Step 6: The operation completes filling its output control

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Henderson, A., Nicolescu, R., Dinneen, M.J. et al. Programmable and parallel water computing. J Membr Comput 5, 25–54 (2023). https://doi.org/10.1007/s41965-022-00114-5

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