Petri Net + Nested Relational Calculus = Dataflow

Abstract

Abstract. In this paper we propose 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 -Petri nets, which are responsible for the organization of the processing tasks, and -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 hierarchical manner, according to a set of refinement rules we propose, are sound : 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 always process all of the input data, leave no "debris data" behind and the output is always eventually computed.

Reo + mCRL2 : A framework for model-checking dataflow in service compositions

“…However, we do not limit our approach to structural verification of workflow models, but target at time-and data-aware analysis, while Raedts et al's translation represents only the number of data tokens in Petri-nets, but not their content. For dataflow modeling, Hidders et al [31,32] extend Petri nets with nested relational calculus, a database query language over composite data types. The authors introduce a set of refinement rules which, being applied hierarchically, guarantee that the final workflow net is sound, i.e., initiated and terminated with a single token in the input and output nodes, all input data is processed, no 'debris data' is left behind and the output is always eventually computed.…”

“…Similar to this approach, we deal with concrete data items rather than abstract tokens. However, [31,32] do not provide integration with model checking tools for verification of the constructed dataflow models. Trčka et al [51] consider workflow correctness criteria analyzing Petri net-based models extended with 'read', 'write' and 'destroy' operations to enable mixed control-and dataflow analysis.…”

“…However, as Petri nets are token-driven by nature, they are on their own insufficient for dataflow verification. While the routing of messages in a process model can be adequately captured with traditional Petri nets, the data manipulation aspect requires more powerful concepts [31,51].…”

Modeling and Storing Scientific Protocols

“…Zhao et al [14] propose an XML-based virtual data language for a typed and compositional protocol specification, with mapping descriptors between the design and implementation. A formal graphical language for hierarchical modeling of protocols has also been proposed in Hidders et al [15], and combines Petri nets with operators and typing system from nested relational calculus.…”

Efficient provenance storage over nested data collections

“…For instance, many systems (e.g., [27,32,36,31,23,39,29,30,18,26]) support actors that make only small changes or updates to incoming data, passing on some or all of their input to downstream actors. Thus, if invocation a above retains within its output y some unchanged substructure s from its input x, denoted as 2 x = (s ⊕ x 0 ), y = (s ⊕ y 0 ) then s will be stored twice: once in the trace record in(x, a) (call this occurrence s x ) and once in out(a, y) (call this occurrence s y ).…”