A Protocol for Solutions to DP-Complete Problems through Tissue Membrane Systems

Considering a class R comprising recognizer membrane systems with the capability of providing polynomial-time and uniform solutions for NP-complete problems (referred to as a presumably efficient class), the corresponding polynomial-time complexity class PMCR encompasses both the NP and co - NP classes. Specifically, when R represents the class of recognizer presumably efficient cell-like P systems that incorporate object evolution rules, communication rules, and dissolution rules, PMCR includes both the DP and co - DP classes. Here, DP signifies the class of languages that can be expressed as the difference between any two languages in NP (it is worth noting that NP subset of DP and co - NP subset of co - DP). As DP-complete problems are believed to be more complex than NP-complete problems, they serve as promising candidates for studying the P vs NP problem. This outcome has previously been established within the realm of recognizer P systems with active membranes. In this paper, we extend this result to encompass any class R of presumably efficient recognizer tissue-like membrane systems by presenting a detailed protocol for transforming solutions of NP-complete problems into solutions of DP-complete problems.

Automated summary

This paper discusses the class R of recognizer membrane systems that can provide polynomial-time and uniform solutions for NP-complete problems, defining it as an efficient class. By representing R as a class of efficient recognizer cell-like P systems with object evolution rules, communication rules, and dissolution rules, the polynomial-time complexity class PMCR is obtained, encompassing both the NP and co-NP classes. The DP class, which includes languages that can be expressed as the difference between any two languages in NP, is considered as a more complex class than the NP class and serves as promising candidates for studying the P vs NP problem. This paper extends previous results to include any class R of efficient recognizer tissue-like membrane systems and presents a detailed protocol for transforming solutions of NP-complete problems into solutions of DP-complete problems.