We further develop water computing as a variant of P systems. We propose an improved modular design, which duplicates the main water flows by associated control flows. We first solve the three open problems of the previous design by demonstrating: how functions can be stacked without a combinatorial explosion of valves; how termination of the system can be detected; and how to reset the system. We then prove that the system is Turing complete by modelling the construction of \(\mu\)-recursive functions. The new system is based on directed acyclic graphs, where tanks are nodes and pipes are arcs; there are no loops anymore, waterfalls strictly in a ‘top down’ direction. Finally, we demonstrate how our water tank system can be viewed as a restricted version of cP systems. We conclude with a list of further challenging problems.
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Henderson, A., Nicolescu, R., Dinneen, M.J. et al. Turing completeness of water computing. J Membr Comput 3, 182–193 (2021). https://doi.org/10.1007/s41965-021-00081-3
- Water-based computing
- Membrane systems