Natural Computing ( IF 2.1 ) Pub Date : 2022-10-19 , DOI: 10.1007/s11047-022-09924-z David Orellana-Martín , Luis Valencia-Cabrera , Bosheng Song , Linqiang Pan , Mario J. Pérez-Jiménez
In the framework of Membrane Computing, several efficient solutions to computationally hard problems have been given. To find new borderlines between families of P systems that can solve them and the ones that cannot is an important task to tackle the P versus NP problem. Adding syntactic and/or semantic ingredients can mean passing from non-efficiency to presumed efficiency. Here, we try to get narrow frontiers, setting the stage to adapt efficient solutions from a family of P systems to another one. In order to do that, a solution to the SAT problem is given by means of a family of tissue P systems with evolutional symport/antiport rules and cell separation with the restriction that both the left-hand side and the right-hand side of the rules have at most two objects; that is, with recognizer P systems from \({\mathcal {TSEC}}(2, 2)\). This result improves a previous one, when 3 objects could be used in the left-hand side of the evolutional communication rules
中文翻译:
具有进化通信规则的组织 P 系统,左侧有两个对象
在膜计算的框架中,已经给出了几种计算难题的有效解决方案。在可以解决它们的 P 系统家族和不能解决它们的 P 系统家族之间找到新的边界是解决P与NP问题的一项重要任务。添加句法和/或语义成分可能意味着从非效率过渡到假定的效率。在这里,我们试图获得狭窄的边界,为将有效解决方案从 P 系统家族适应另一个系统做好准备。为了做到这一点,SAT的解决方案问题是通过具有进化同向/反向规则和细胞分离的组织 P 系统家族给出的,其限制是规则的左侧和右侧最多有两个对象;也就是说,使用来自\({\mathcal {TSEC}}(2, 2)\)的识别器 P 系统。这个结果改进了之前的结果,当进化通信规则的左侧可以使用 3 个对象时