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A Representation of Processes of Petri Nets by Matrices

A correspondence between processes of Petri nets and partitioned matrices over freely generated semirings is described. This correspondence implies a correspondence between operations of composing processes sequentially and in parallel and operations of multiplying and juxtaposing the respective partitioned matrices. It results in a characterization of partitioned matrices corresponding to processes of a given net and, consequently, allows one to represent processes by their matrices.