P systems with active membranes are a class of computation models in the area of membrane computing, which are inspired from the mechanism by which chemicals interact and cross cell membranes. In this work, we consider a normal form of P systems with active membranes, called cell-like P systems with polarizations and minimal rules, where rules are minimal in the sense that an object evolves to exactly one object with the application of an evolution rule or a communication rule, or an object evolves to two objects that are assigned to the two new generated membranes by applying a division rule. The present work investigates the computational power of P systems with polarizations and minimal rules. Specifically, results about Turing universality and non-universality are obtained with the combination of the number of membranes, the number of polarizations, and the types of rules. We also show that polarizationless P systems with minimal rules are equivalent to Turing machines working in a polynomial space, that is, the class of problems that can be solved in polynomial time by polarizationless P systems with minimal rules is equal to the class PSPACE.

具有活性膜的P系统是膜计算领域中的一类计算模型，其灵感来自化学物质相互作用和穿过细胞膜的机制。在这项工作中，我们考虑具有活动膜的P系统的正常形式，即具有极化和最小规则的类细胞P系统，其中规则在某种意义上是最小的，即对象通过应用进化规则而演化为一个对象或通信规则，或对象通过应用划分规则演变为分配给两个新生成的膜的两个对象。本工作研究具有极化和最小规则的P系统的计算能力。具体来说，结合膜的数量获得关于图灵通用性和非通用性的结果，极化的数量和规则的类型。我们还表明，具有最小规则的无极化P系统等同于在多项式空间中工作的图灵机，也就是说，具有最小规则的无极化P系统可以在多项式时间内解决的问题的类别等于该类空格。