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We show a collection of scripts, called $G$-strongly positive scripts, whichis used to recognize critical configurations of a chip firing game (CFG) on amulti-digraph with a global sink. To decrease the time of the process ofrecognition caused by the stabilization we present an algorithm to find theminimum G-strongly positive script. From that we prove the non-stability ofconfigurations obtained from a critical configuration by firing inversely anynon-empty multi-subset of vertices. This result is a generalization of a veryrecent one by Aval \emph{et.al} which is applied for CFG on undirected graphs.Last, we give a combinatorial proof for the duality between critical andsuper-stable configurations.

$G$-strongly positive scripts and critical configurations of chip firing games on digraphs