Finding AND-OR Hierarchies in Workflow Nets

TL;DR

This paper introduces AND-OR reduction for workflow nets, enabling hierarchical analysis and verification of net properties, with a polynomial-time algorithm ensuring consistent results despite non-determinism.

Contribution

It formalizes AND-OR reduction, proves its confluence, and provides an efficient algorithm for hierarchical analysis and verification of workflow nets.

Findings

AND-OR reduction preserves soundness of WF nets.

The reduction is confluent up to isomorphism.

A polynomial-time algorithm computes the unique reduction result.

Abstract

This paper presents the notion of AND-OR reduction, which reduces a WF net to a smaller net by iteratively contracting certain well-formed subnets into single nodes until no more such contractions are possible. This reduction can reveal the hierarchical structure of a WF net, and since it preserves certain semantical properties such as soundness, it can help with analysing and understanding why a WF net is sound or not. The reduction can also be used to verify if a WF net is an AND-OR net. This class of WF nets was introduced in earlier work, and arguably describes nets that follow good hierarchical design principles. It is shown that the AND-OR reduction is confluent up to isomorphism, which means that despite the inherent non-determinism that comes from the choice of subnets that are contracted, the final result of the reduction is always the same up to the choice of the identity of the nodes. Based on this result, a polynomial-time algorithm is presented that computes this unique result of the AND-OR reduction. Finally, it is shown how this algorithm can be used to verify if a WF net is an AND-OR net.