Membrane computing with water

Abstract

We introduce water tank systems as a new class of membrane systems inspired by a decentrally controlled circulation of water or other liquids throughout cells called tanks and capillaries called pipes. To our best knowledge, this is the first proposal addressing the behavioural principle of floating and stored water for modelling of information processing in terms of membrane computing. The volume of water within a tank stands for a non-negative rational value when acting in an analogue computation or it can be interpreted in a binary manner by distinction of “(nearly) full” or “(nearly) empty”. Water tanks might be interconnected by pipes for directed transport of water. Each pipe can be equipped with valves which in turn either fully open or fully close the hosting pipe according to permanent measurements whether the filling level in a dedicated water tank exceeds a certain threshold or not. We demonstrate dedicated water tank systems together with simulation case studies: a ring oscillator for generation of clock signals and for iteratively making available amounts of water in a cyclic scheme, analogue arithmetics by implementation of addition, non-negative subtraction, division, and multiplication complemented by systems in binary mode for implementation of selected logic gates.

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