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Petri nets is the well-known mathematical tool for the modeling and verification of parallel systems of all kind. Multiprocess Petri multinets with time stamps (MPTSM) are the newly introduced class of low-level Petri nets, whose definition and the properties are the main topic of this article; they generalize the properties of P/T Petri multiprocess multinets in the area of design, modeling and verification of generally parallel programming systems with the discrete time. The MPTSM with the support of the ASYNC-C...