From SAT to SAT-UNSAT using P systems with dissolution rules

DP is the class of problems that are the differences between two languages from NP. Most difficult problems from DP are called DP-complete problems, that can be seen as the conjunction of an NP-complete problem and a co-NP-complete problem. It is easy to see that the problem P vs NP is equivalent to...

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Bibliographic Details
Authors: Riscos Núñez, Agustín, Valencia Cabrera, Luis
Format: article
Status:Published version
Publication Date:2022
Country:España
Institution:Universidad de Sevilla (US)
Repository:idUS. Depósito de Investigación de la Universidad de Sevilla
OAI Identifier:oai:idus.us.es:11441/134910
Online Access:https://hdl.handle.net/11441/134910
https://doi.org/10.1007/s41965-022-00095-5
Access Level:Open access
Keyword:Complexity class DP
Membrane computing
Product problem
Satisfability problem
Description
Summary:DP is the class of problems that are the differences between two languages from NP. Most difficult problems from DP are called DP-complete problems, that can be seen as the conjunction of an NP-complete problem and a co-NP-complete problem. It is easy to see that the problem P vs NP is equivalent to the problem P vs DP, and therefore DP-complete problems would be better candidates to attack the conjecture, since they seem to be harder than NP-complete problems. In this paper, a methodology to transform an efficient solution of an NP-complete problem into an efficient solution of a DP-complete problem is applied. More precisely, a solution to SAT is given by means of a uniform family of recognizer polarizationless P systems with active membranes with dissolution rules and division rules for both elementary and non-elementary membranes, and later it is transformed into a solution to the problem SAT-UNSAT.