Timed Homeostasis Tissue-Like P Systems With Evolutional Symport/Antiport Rules

Tissue-like P systems are a type of distributed parallel computing models inspired by actual biological tissue. In this paper, we consider a new variant of tissue-like P systems, which is called tissue-like P systems with evolutional symport/antiport rules. Unlike traditional models of this type, in the new P systems, objects can change during transmission. In biology, an organism that is in “homeostasis” reduces its dependence on external conditions, thereby keeping it relatively constant and maintaining a relatively stable internal environment. In our work, we remove the assumption that the quantity of objects in the environment is infinite, reducing the influence of the environment on this system, so the environment no longer provides powerful energy for cells. Moreover, the time-free mode is introduced into this type of P systems, which makes the constructed systems more robust. We investigate the computational power and computational efficiency of the constructed system. Specifically, by simulating register machines, such a P system can generate any Turing computable set of numbers. In addition, we prove that this constructed system can efficiently solve the $\mathcal {SAT} $ problem. Although we restrict P systems and consider time-free manner, the results show that this system is not only Turing universal, but also can solve NP-complete problem.