Properties of SN P system and its Configuration Graph

TL;DR

This paper investigates the behavioral and structural properties of SN P systems without delay, introducing the configuration graph and matrix concepts to analyze their dynamics and structure based on the fundamental state equation.

Contribution

It introduces the configuration graph and matrix frameworks for SN P systems without delay, advancing understanding of their behavior and structure.

Findings

Characterization of SN P system behavior via configuration graphs.

Structural analysis using the matrix $M_{\Pi}$.

Preliminary insights into properties dependent on the fundamental state equation.

Abstract

Several studies have been reported in the literature about SN P system and its variants. Often, the results provide universality of various variants and the classes of languages that these variants generate and recognize. The state of SN P system is its configuration. We refer to our previous result on reachability of configuration as the {\it Fundamental state equation for SN P system.} This paper provides a preliminary investigation on the behavioral and structural properties of SN P system without delay that depend primarily to this fundamental state equation. Also, we introduce the idea of configuration graph $CG_{\Pi}$ of an SN P system $\Pi$ without delay to characterize behavioral properties of $\Pi$ with respect to $CG_{\Pi}.$ The matrix $M_{\Pi}$ of an SN P system $\Pi$ without delay is used to characterize structural properties of $\Pi.$