Petri nets are a powerful formalism that can model system properties, define complex $($but potentially infinite$)$ Kripke structures, express languages, and more. In class, we introduced several techniques to analyze Petri nets in meaningful ways. Given the Petri net M below, answer the following questions:Petri nets are a powerful formalism that can model system properties, define complex $($but potentially

infinite$)$ Kripke structures, express languages, and more. In class, we introduced several techniques to

analyze Petri nets in meaningful ways. Given the Petri net $M$ below, answer the following questions:

Provide the minimum coverability set for $M$ given initial marking $[10000].$

Algorithm $6\mathrm{.}2\mathrm{.}2$ can $($and probably should!$)$ be used to check your results.

Let $K$ be the Kripke structure generated from $M$ with initial marking $03110($after we add a selfloop

to any dead marking$).$ In $K,$ does $[03110]|==AP(p_4=0)?$ Does $[03110]|==AF(p_2=0^{{?}^{?}}{p}_4=0)?$

Let the language generated by a Petri net with initial marking $m_{\text{i}\text{n}\text{i}\text{t}}$ transition set $T,$ and transition

$30pt$

labeling function $$:$T\{c\}$ be