Narrow Results

We consider tissue P systems with symport/antiport rules and investigate their computational power when using only a (very) small number of symbols and cells. Even when using only one symbol, we need at most six (seven when allowing only one channel between a cell and the environment) cells to generate any recursively enumerable set of natural numbers. On the other hand, with only one cell we can only generate regular sets when using one channel with the environment, whereas one cell with two channels between the cell and the environment obtains computational completeness with five symbols. Between these extreme cases of one symbol and one cell, respectively, there seems to be a trade-off between the number of cells and the number of symbols. For example, for the case of tissue P systems with two channels between a cell and the environment we show that computational completeness can be obtained with two cells and three symbols as well as with three cells and two symbols, respectively. Moreover, we also show that some variants of tissue P systems characterize the families of finite or regular sets of natural numbers.

We give a survey on the contribution of our research group to the cell theory of weighted Coxeter groups. We present some detailed accounts for the description of cells of the affine Weyl group ${\tilde{C}}_n$ in the quasi-split case and a brief account for that of the affine Weyl group ${\tilde{B}}_n$ in the quasi-split case and of the weighted universal Coxeter group in general case.