Tissue-like P Systems with Channel-States

Abstract

We consider tissue-like P systems with states associated with the links (we call them synapses) between cells, controlling the passage of objects across the links. We investigate the computing power of such devices for the case of using - in a sequential manner - antiport rules of small weights. Sys- tems with two cells are proven to be universal when having arbitrarily many states and minimal antiport rules, or two states, and antiport rules of weight two. Also the systems with arbitrarily many cells, three states, and minimal antiport rules are universal. In contrast, the systems with one cell and any number of states and rules of any weight only compute Parikh sets of ma- trix languages (generated by matrix grammars without appearance checking); characterizations of Parikh images of matrix languages are obtained for such one-cell systems with antiport rules of a reduced weight. A series of open problems are also formulated.