Time-free solution to independent set problem using P systems with active membranes

TL;DR

This paper presents a novel time-free approach using P systems with active membranes to solve the independent set problem, aligning computational models more closely with biological processes that have variable timing.

Contribution

It introduces a time-free method for solving the independent set problem with P systems, removing the assumption of synchronized rule execution based on a global clock.

Findings

Successfully solves the independent set problem without relying on execution time assumptions

Demonstrates biological plausibility by modeling variable process durations

Provides a new framework for membrane computing that better reflects natural cellular processes

Abstract

Membrane computing is a branch of natural computingwhich abstracts fromthe structure and the functioning of living cells. The computation models obtained in the field of membrane computing are usually called P systems. P systems have been used to solve computationally hard problems efficiently on the assumption that the execution of each rule is completed in exactly one time-unit (a global clock is assumed for timing and synchronizing the execution of rules). However, in biological reality, different biological processes take different times to be completed, which can also be influenced by many environmental factors. In this work, with this biological reality, we give a time-free solution to independent set problemusing P systems with active membranes, which solve the problem independent of the execution time of the involved rules.