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 clas...
| Authors: | , , , , |
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| Format: | article |
| Status: | Published version |
| Publication Date: | 2023 |
| Country: | España |
| Institution: | Universidad de Sevilla (US) |
| Repository: | idUS. Depósito de Investigación de la Universidad de Sevilla |
| OAI Identifier: | oai:idus.us.es:11441/166046 |
| Online Access: | https://hdl.handle.net/11441/166046 https://doi.org/10.3390/math11132797 |
| Access Level: | Open access |
| Keyword: | Complexity class DP Membrane computing Tissue P systems |
| Summary: | 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 DP and co NP 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. |
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