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Fundamenta Informaticae
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Alan Turing began a new area in science; he discovered that there are universal computers, which in principal are very simple. Up to now this is the basis of a modern computing theory and practice. In the paper one considers Turing computability in the frame of P (membrane) systems and other distributive systems. An overview of the recent results about small universal P and DNA systems and some open problems and possible directions of investigation are presented.