Parallel Multiset Rewriting Systems with Distorted Rules

Cristina Sburlan,Dragoş-Florin Sburlan

doi:10.3390/pr9020347

Abstract

Most of the parallel rewriting systems which model (or which are inspired by) natural/artificial phenomena consider fixed, a priori defined sets of string/multiset rewriting rules whose definitions do not change during the computation. Here we modify this paradigm by defining level-t distorted rules—rules for which during their applications one does not know the exact multiplicities of at most t∈N species of objects in their output (although one knows that such objects will appear at least once in the output upon the execution of this type of rules). Subsequently, we define parallel multiset rewriting systems with t-distorted computations and we study their computational capabilities when level-1 distorted catalytic promoted rules are used. We construct robust systems able to cope with the level-1 distortions and prove the computational universality of the model.

Highlights

Biological, social, and economic life are governed by different levels of uncertaintyCitation: Sburlan, C.; Sburlan, D.-F. which usually regard the epistemic cases and facts related to incomplete knowledge due Parallel Multiset Rewriting Systems to unknown/faulty information
We considered the simplified version of catalytic P systems with promoters and/or inhibitors at the level of the rules which does not take into account the hierarchical membrane structure— we explored the computational capabilities of parallel multiset rewriting systems with catalysts and promoters/inhibitors whose rewriting rules are distorted during computations
We present parallel multiset rewriting systems as a particular case of P systems

Summary

Introduction

Biological, social, and economic life are governed by different levels of uncertainty. The issue of building rewriting systems that are able to cope with uncertainty (at the level of parallelism of the rewriting, or regarding the execution time of the rewriting rules, or the non-determinism) and solve problems was addressed in several papers (see [1,2,3,4,5,6]). Another approach to model uncertainty was to dynamically construct rules at each step during the computation. In Conclusions we discuss several open problems and future lines of research

Prerequisites

Parallel Multiset Rewriting Systems

Towards “Distorted” Computations

Conclusions