A new method to simulate restricted variants of polarizationless P systems with active membranes

Zsolt Gazdag,Gábor Kolonits

doi:10.1007/s41965-019-00024-z

Zsolt Gazdag, Gábor Kolonits

Open Access

https://doi.org/10.1007/s41965-019-00024-z

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Abstract

According to the P conjecture by Gh. Păun, polarizationless P systems with active membranes cannot solve {mathbf {NP}}-complete problems in polynomial time. The conjecture is proved only in special cases yet. In this paper we consider the case where only elementary membrane division and dissolution rules are used and the initial membrane structure consists of one elementary membrane besides the skin membrane. We give a new approach based on the concept of object division polynomials introduced in this paper to simulate certain computations of these P systems. Moreover, we show how to compute efficiently the result of these computations using these polynomials.

Highlights

P systems with active membranes, introduced in [23], are among the most investigated variants of P systems
Using P 1, we show how to calculate in polynomial time which and how many objects are released to the skin membrane in each step of C (Theorem 1)
We show that the multiset content of the skin membrane of at the end of so-called divisiondriven computations can be computed in polynomial time in nm

Summary

Introduction

P systems with active membranes, introduced in [23], are among the most investigated variants of P systems. To determine the result of a computation in this case it is enough to check whether a distinguished object is reachable from certain objects in the dependency graph Using dependency graphs it was shown in [10] that polarizationless P systems with active membranes using no dissolution rules and working in polynomial time can solve only problems in. The P systems are deterministic, can use all types of rules except send-in communication rules, and the membrane structure is such that the skin contains only elementary membranes In these papers the authors used these generalizations of dependency graphs to simulate a reasonable small part of the configurations in a computation of the investigated P systems. A generalization to P systems having send-out communication rules and a more general initial membrane structure seems to be achievable as it is discussed in the Conclusions section

Preliminaries

Results

Conclusions