Over the last few years, a new methodology to address the P versus NP problem has been developed, based on searching for borderlines between the nonefficiency of computing models (only problems in class P can be solved in polynomial time) and the presumed efficiency (ability to solve NP-complete problems in polynomial time). These borderlines can be seen as frontiers of efficiency, which are crucial in this methodology. “Translating,” in some sense, an efficient solution in a presumably efficient model to an efficient solution in a nonefficient model would give an affirmative answer to problem P versus NP. In the framework of Membrane Computing, the key of this approach is to detect the syntactic or semantic ingredients that are needed to pass from a nonefficient class of membrane systems to a presumably efficient one. This paper deals with tissue P systems with communication rules of type symport/antiport allowing the evolution of the objects triggering the rules. In previous works, frontiers of efficiency were found in these kinds of membrane systems both with division rules and with separation rules. However, since they were not optimal, it is interesting to refine these frontiers. In this work, optimal frontiers of the efficiency are obtained in terms of the total number of objects involved in the communication rules used for that kind of membrane systems. These optimizations could be easier to translate, if possible, to efficient solutions in a nonefficient model.

中文翻译：

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利用进化交流规则调整组织P系统效率的前沿

在过去的几年中，基于寻找计算模型的非效率（只能在多项式时间内解决P类问题）之间的界限，已经开发了一种解决P与NP问题的新方法。（在多项式时间内解决NP完全问题）。这些边界可以看作是效率的前沿，这在此方法中至关重要。从某种意义上说，“将”可能有效的模型中的有效解决方案“转换为”非效率模型中的有效解决方案，将为问题P与NP给出肯定的答案。在膜计算的框架中，此方法的关键是检测从无效类的膜系统传递到大概有效的膜系统所需的句法或语义成分。本文处理的组织P系统具有类型为同向/反向的通信规则，允许触发规则的对象的进化。在以前的工作中，在具有划分规则和分离规则的这类膜系统中发现了效率前沿。但是，由于它们不是最佳的，因此改进这些领域很有趣。在这项工作中，根据用于该类膜系统的通信规则所涉及的对象总数，获得了效率的最佳边界。如果可能的话，这些优化可能更容易翻译，