Tissue P systems provide distributed parallel devices inspired by actual biological reality, where communication rules are used for object exchange between cells (or between cells and the environment). In such systems, the environment continuously provides energy to cells, so the cells are very dependent on the objects in the environment. In biology, there is a mechanism called homeostasis, that is, an internal organism is independent from the external conditions, thus keeping itself relatively stable. Inspired by this biological fact, in this paper, we assume that the environment no longer provides energy for cells, introducing multiset rewriting rules into tissue P systems, thereby constructing a novel computational model called homeostasis tissue-like P systems. Based on the model, we construct two uniform solutions in feasible time. One solution is constructed to solve the 3-coloring problem in linear time in standard time, and the other solution is constructed to solve the $\mathcal {SAT} $ problem with communication rules and multiset rewriting rules of the length at most 3 in time-free mode. Moreover, we prove that the constructed system can generate any Turing computable set of numbers using communication rules and multiset rewriting rules with a maximal length 3, working in the mode of standard time and time-free, respectively. The results show that our constructed system does not rely on the environment and reflects the phenomenon of biological homeostasis. In addition, although the system runs in time-free way, it not only has Turing university, but also can effectively solve NP -complete problem.

中文翻译：

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稳态组织样 P 系统。

组织 P 系统提供受实际生物现实启发的分布式并行设备，其中通信规则用于细胞之间（或细胞与环境之间）的对象交换。在这样的系统中，环境不断地为细胞提供能量，因此细胞非常依赖环境中的物体。在生物学中，有一种机制叫做稳态，即一个有机体内部独立于外部条件，从而保持自身相对稳定。受这一生物学事实的启发，在本文中，我们假设环境不再为细胞提供能量，将多组重写规则引入组织 P 系统，从而构建了一种称为稳态组织样 P 系统的新型计算模型。基于该模型，我们在可行时间内构造了两个统一解。 $\mathcal {SAT} $ 无时间模式下长度最多为3的通信规则和多集重写规则的问题。此外，我们证明构建的系统可以使用通信规则和最大长度为 3 的多集重写规则生成任何图灵可计算的数字集，分别工作在标准时间和无时间模式下。结果表明，我们构建的系统不依赖于环境，反映了生物体内平衡的现象。此外，该系统虽然以无时间方式运行，但它不仅具有图灵大学，还可以有效解决NP - 完全问题。