Translating Workflow Nets to Process Trees: An Algorithmic Approach
Abstract
:1. Introduction
2. Preliminaries
2.1. Basic Notation
2.2. Workflow Nets
- 1.
- ;is the unique source place.
- 2.
- ;is the unique sink place.
- 3.
- Each elementis on a path fromto.
- 1.
- is safe,i.e., ,
- 2.
- can always be reached, i.e.,.
- 3.
- Eachis enabled, at some point, i.e.,.
2.3. Process Trees
- 1.
- ; an (non-observable) activity,
- 2.
- , for, , whereare process trees;
3. Translating Workflow Nets to Process Trees
3.1. Overview
3.2. PTree-Nets and Their Unfolding
- 1.
- ,
- 2.
- ,
- 3.
- ,
- 4.
- . (Since functions are binary Cartesian products, we write set operations here).
3.3. Pattern Reduction
3.3.1. Sequential Pattern
- 1.
- , transitionenables; and
- 2.
- , enabling is unique,
3.3.2. Exclusive Choice Pattern
- 1.
- , all pre-sets are shared among the members of the pattern;
- 2.
- , all post-sets are shared among the members of the pattern; and
- 3.
- , self-loops are not allowed,
3.3.3. Concurrent Pattern
- 1.
- , no interaction between the member’s pre-sets;
- 2.
- , no interaction between the member’s post-sets;
- 3.
- , pre-set places uniquely connect to a member;
- 4.
- , post-set places uniquely connect to a member;
- 5.
- , members do not influence other members;
- 6.
- , member’s pre-sets share their pre-set;
- 7.
- , member firing does not affect other members;
- 8.
- , member’s post-sets share their post-set;
- 9.
- , pre-sets of enablers are equal;
- 10.
- , post-sets of enablers are equal,
3.3.4. Loop Pattern
- 1.
- , pre-set ofis the post-set of;
- 2.
- , pre-set ofis the post-set of;
- 3.
- , is the only transition in the post-set of its pre-set;
- 4.
- ; , is the only transition in the pre-set of its post-set,
3.4. Algorithm
Algorithm 1: WF-net reduction |
4. Evaluation
4.1. Implementation
4.2. Experimental Setup
4.3. Results
5. Related Work
6. Discussion
6.1. Extensibility
6.2. Relation to Refined Process Structure Tree
6.3. Reducibility of WF-Nets
7. Conclusions
Author Contributions
Funding
Conflicts of Interest
References
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van Zelst, S.J.; Leemans, S.J.J. Translating Workflow Nets to Process Trees: An Algorithmic Approach. Algorithms 2020, 13, 279. https://doi.org/10.3390/a13110279
van Zelst SJ, Leemans SJJ. Translating Workflow Nets to Process Trees: An Algorithmic Approach. Algorithms. 2020; 13(11):279. https://doi.org/10.3390/a13110279
Chicago/Turabian Stylevan Zelst, Sebastiaan J., and Sander J. J. Leemans. 2020. "Translating Workflow Nets to Process Trees: An Algorithmic Approach" Algorithms 13, no. 11: 279. https://doi.org/10.3390/a13110279