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Linear constraint transformation is an essential step to solve the forbiddenstate problem in Petri nets that contain uncontrollable transitions. This workstudies the equivalent transformation from a legal-marking set to itsadmissible-marking set given such a net. First, the concepts of anescaping-marking set and a transforming marking set are defined. Based on them,two algorithms are given to compute the admissible-marking set and thetransforming marking set, which establish the theoretical foundation for theequivalent transformation of linear constraints. Second, the theory about theequivalent transformation of a disjunction of linear constraints imposed toPetri nets with uncontrollable transitions is established. Third, two rules aregiven to decide the priority of transitions for transformation. Finally, thetransformation procedure from a given linear constraint to a logic expressionof linear constraints that can describe its entire admissible-marking set isillustrated via two examples.

Transformation From Legal-marking Set to Admissible-marking Set of Petri Nets With Uncontrollable Transitions