On Generating *-Sound Nets with Substitution

Abstract

We present a method for hierarchically generating sound workflow nets by substitution of nets with multiple inputs and outputs. We show that our method is correct and generalizes the class of nets generated by other hierarchical approaches. We identify a notion of soundness that is preserved by such substitutions and correct a small omission in an earlier similar method.

On Determining the AND-OR Hierarchy in Workflow Nets

“…Quickly several alternative definitions of soundness, varying in strictness and verification difficulty, emerged. Examples of these are weak soundness [12,13], relaxed soundness [6], lazy soundness [18], k-soundness and generalised soundness [29,28], up-to-k-soundness [27] and substitution soundness [20]. Informally, the original notion of soundness guarantees two properties of the net.…”

“…In earlier research [20] we have proposed a new notion of soundness, namely the substitution soundness or sub-soundness for short. It is similar to k-and *-soundness studied in [29], but captures exactly the conditions necessary for building complex workflow nets by following a structured approach where subsystems with multiple inputs and outputs are used as building blocks of larger systems.…”

“…Although stronger soundness properties may be desirable, they are often also more difficult to verify. For this reason, a method is introduced in [20] for systematically constructing workflow nets so that they are guaranteed to satisfy the sub-soundness property. This method is in principle, and in effect, similar to methods employed in software engineering, where complexity is tackled by separation of concerns and encapsulation, and systems are divided into building blocks such as modules, objects and functions, which in turn can be decomposed further.…”

“…In programming the ideas of using macros, subroutines, procedures, functions, and later on, classes, proved that even extremely complex systems can be programmed and maintained in a practical and effective manner. Such structurisation was successfully applied to designing complex Petri nets [33,21,7,1,8,17] and workflow nets [2,23,20]. As with general programming, the system is composed of small, separated fragments, which are easier to understand and maintain.…”

“…The class of nets we introduced in [20] is called the class of AND-OR nets (see Section 3). This class is larger and more general than other classes of workflow nets generated with a similar type of structural approach, as presented for example in [29,2].…”