Enhanced Membrane Computing Algorithm for SAT Problems Based on the Splitting Rule

Boolean propositional satisfiability (SAT) problem is one of the most widely studied NP-complete problems and plays an outstanding role in many domains. Membrane computing is a branch of natural computing which has been proven to solve NP problems in polynomial time with a parallel compute mode. This paper proposes a new algorithm for SAT problem which combines the traditional membrane computing algorithm of SAT problem with a classic simplification rule, the splitting rule, which can divide a clause set into two axisymmetric subsets, deal with them respectively and simultaneously, and obtain the solution of the original clause set with the symmetry of their solutions. The new algorithm is shown to be able to reduce the space complexity by distributing clauses with the splitting rule repeatedly, and also reduce both time and space complexity by executing one-literal rule and pure-literal rule as many times as possible.

Survival forests for data with dependent censoring

Tree-based methods are very powerful and popular tools for analysing survival data with right-censoring. The existing methods assume that the true time-to-event and the censoring times are independent given the covariates. We propose different ways to build survival forests when dependent censoring is suspected, by using an appropriate estimator of the survival function when aggregating the individual trees and/or by modifying the splitting rule. The appropriate estimator used in this paper is the copula-graphic estimator. We also propose a new method for building survival forests, called p-forest, that may be used not only when dependent censoring is suspected, but also as a new survival forest method in general. The results from a simulation study indicate that these modifications improve greatly the estimation of the survival function in situations of dependent censoring. A real data example illustrates how the proposed methods can be used to perform a sensitivity analysis.