Tissue P systems with states in cells

Tissue-like P systems with channel states are a type of classical membrane systems in which objects transferred among regions are controlled by states placed in the channels between regions. However, an important biological fact is the existence of a "barrier" to the diffusion of signal molecules, which tend to remain confined to some particular micro-habitat. This feature allows quorum sensing to convey information about the physiological state of spatially separated sub-populations. Therefore, in this article, we design a novel class-variant of P systems named tissue P systems with states in cells (TSIC P systems). Here, each cell contains one and only one state at any moment (the environment has no state), and objects transferred among regions are controlled by states (or a state) that are placed in the corresponding cells (or a cell). We discuss the computability theory of TSIC P systems by showing that Turing universality is acquired by TSIC P systems, which are worked both in a flat maximal parallelism and in a maximal parallelism. In addition, when cell division is considered in TSIC P systems, then tissue P systems with states in cells and cell division (TSICD P systems) are constructed. The (presumed) computational efficiency of TSICD P systems is reached by offering a uniform solution to the satisfiability problem.