# Petri net analysis (attainability)

how to analyse safe petri net for attainability? (i need algorithm)

I have an oriented multigraph $\mathbb{G}$.

$A$ - adjacency matrix.

$m$ - the count of input elements.

$n$ - the count of vertices in $\mathbb{G}$

let numerate input elements $b_i,\; i\in\{1..m\}$ and vertexes $v_j,\; j\in\{1..n\}$

limitation $m \leq n$ (safe petri net)

let make marker, which connect input element $b_i$ and vertex $v_j$, where it stand and define it like this: $(b_i,v_j)$

first state of petri net is $M_0$: $\{(b_i,v^0_j),i\in\{1..m\},\;j\in\{k_1..k_m\},\; k_i \in \{1..n\},\; k_i\not = k_j\}$

last state of petri net is $M_1$: $\{(b_i,v^1_j),i\in\{1..m\},\;j\in\{p_1..p_m\},\; p_i\in\{1..n\},\; p_i \not = p_j\}$

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