Alive Petri net

Alive Petri net --- живая сеть Петри. A Petri net[math]\displaystyle{ N }[/math] is called alive iff whenever [math]\displaystyle{ m }[/math] is a reachable marking for [math]\displaystyle{ N }[/math] and [math]\displaystyle{ t }[/math] is a transition of [math]\displaystyle{ N }[/math], it is possible for [math]\displaystyle{ N }[/math] to reach, starting from [math]\displaystyle{ m }[/math], a marking in which [math]\displaystyle{ t }[/math] is enabled.