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Petri nets are widely used to model concurrent software systems. Currently, there are many different kinds of Petri net tools that can analyze system properties such as deadlocks, reachability and liveness. However, most tools are not suitable to analyze data-flow errors of concurrent systems because they do not formalize data information and lack efficient computing methods for analyzing data-flows. Especially when a concurrent system has so many concurrent data operations, these Petri netdoi:10.3390/math9090966 doaj:49d911fcc06e4c7baa45c07bdd4788c9 fatcat:btae5wmyjva3tg7o5ls62ujubu