Abstract

We study the efficiency of the reaction systems in solving NP-complete problems. Due to the fact that standard reaction systems are qualitative, in order to accomplish our aim, in this paper we consider communicating reaction systems with direct communication extended with duration for resources and a mutual exclusion relation between reactions forbidding two reactions to be used in the same step, in parallel. We show that these systems, working in a non-deterministic way, are powerful enough to provide polynomial-time solutions to the subset sum and SAT problems. We consider a semi-uniform approach by constructing a system for each instance of the subset sum and SAT problems and embedding the parameters into the constructed systems.

中文翻译：

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通过反应系统解决子集和和 SAT 问题

摘要

我们研究反应系统解决 NP 完全问题的效率。由于标准反应系统是定性的，为了实现我们的目标，在本文中，我们考虑通过延长资源持续时间的直接通信来通信反应系统，以及反应之间的互斥关系，禁止两个反应在同一个反应中使用步骤，并行。我们证明，这些以非确定性方式工作的系统足够强大，可以为子集和和 SAT 问题提供多项式时间解决方案。我们考虑采用半均匀方法，为子集和和 SAT 问题的每个实例构建一个系统，并将参数嵌入到构建的系统中。