Properties of SN P system and its Configuration Graph

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 $C{G}_{\mathrm{\Pi }}$ of an SN P system $\mathrm{\Pi }$ without delay to characterize behavioral properties of $\mathrm{\Pi }$ with respect to $C{G}_{\mathrm{\Pi }}\mathrm{.}$ The matrix $M_{\mathrm{\Pi }}$ of an SN P system $\mathrm{\Pi }$ without delay is used to characterize structural properties of $\mathrm{\Pi }\mathrm{.}$