Timed Tissue P Systems With Channel States

Tissue P systems with channel states are a variant of tissue P systems that can be employed as highly parallel computing devices, where the channel states can control the movements of objects. In a sense, the time-free approach can improve the robustness of P systems; hence, in this work, we introduce the time-free property into such P systems and explore their computational performances. Specifically, in a time-free manner, it is proved that this type of P systems have Turing universality by using two cells and four channel states with a maximum rule length of 2, or by using two cells and noncooperative symport rules with a maximum rule length of 1. Moreover, in terms of computational efficiency, it is proved that a uniform solution of the satisfiability ( $\mathcal {SAT}$ ) problem can be obtained in a time-free manner by applying noncooperative symport rules with a maximum rule length of 1. The research results of this paper show that a highly robust dynamic membrane computing system is constructed. Theoretically, relative to the existing system, our constructed system can enhance robustness and expand its application scope.