Abstract:
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
µ-recursive functions. The new system is based on directed acyclic graphs, where
tanks are nodes and pipes are arcs; there are no loops anymore, water falls 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.