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Abstract: We present a method for hierarchically generating sound workflow nets by substitution of nets with multiple inputs and outputs. We show that this method is correct and generalizes the class of nets generated by other hierarchical approaches. The method involves a new notion of soundness which is preserved by the generalized type of substitution that is presented in this paper. We show that this notion is better suited than ⁎-soundness for use with the presented type of generalized substitution, since ⁎-soundness is not preserved by it. It is moreover shown that it is in some sense the optimal notion of soundness for the purpose of generating sound nets by the presented type of substitution. [Copyright &y& Elsevier]

Abstract: In this paper we propose DFL—a formal, graphical workflow language for dataflows, i.e., workflows where large amounts of complex data are manipulated, and the structure of the manipulated data is reflected in the structure of the workflow. It is a common extension of (1) Petri nets, which are responsible for the organization of the processing tasks, and (2) nested relational calculus, which is a database query language over complex objects, and is responsible for handling collections of data items (in particular, for iteration) and for the typing system. We demonstrate that dataflows constructed in a hierarchical manner, according to a set of refinement rules we propose, are semi-sound, i.e., initiated with a single token (which may represent a complex scientific data collection) in the input node, terminate with a single token in the output node (which represents the output data collection). In particular they never leave any “debris data” behind and an output is always eventually computed regardless of how the computation proceeds. [Copyright &y& Elsevier]