Reusing artifact-centric business process models: a behavioral consistent specialization approach

Abstract

Process reuse is one of the important research areas that address efficiency issues in business process modeling. Similar to software reuse, business processes should be able to be componentized and specialized in order to enable flexible process expansion and customization. Current activity/control-flow centric workflow modeling approaches face difficulty in supporting highly flexible process reuse, limited by their procedural nature. In comparison, the emerging artifact-centric workflow modeling approach well fits into these reuse requirements. Beyond the classic class level reuse in existing object-oriented approaches, process reuse faces the challenge of handling synchronization dependencies among artifact lifecycles as parts of a business process. In this article, we propose a theoretical framework for business process specialization that comprises an artifact-centric business process model, a set of methods to design and construct a specialized business process model from a base model, and a set of behavioral consistency criteria to help check the consistency between the two process models.

Appendix

In this appendix, we provide detailed proofs of our Lemmas and Theorems.

Proof of Lemma 4.1

We can prove the lemma by construction using the conditions of an AL-fragment (in Definition 4.5), the three inference rules for lifecycle composition (in Definition 3.9), and the soundness condition (in Definition 3.11) to show that if all the conditions of the lemma hold, the composition of all SL-fragments is atomic and sound. We prove the necessity of each of the four conditions as follows.

• For the first condition We have if $\ell^{{\varvec{C}_{\varvec{i}} }} \in \varGamma$ is not an AL-fragment, then the resulted fragment from the composition of $\ell^{{\varvec{C}_{\varvec{i}} }}$ and any other fragment is not an AL-fragment. This is because, based on the three inference rules for the lifecycle composition defined in Definition 3.9, if $\ell^{{\varvec{C}_{\varvec{i}} }}$ has either multiple entry or exit transitions or both, the composition yields multiple transitions for the synchronized product as well. The first condition holds the soundness condition since the AL-fragment is always sound and no synchronization is stated in this condition.

The second, third, and fourth conditions of Lemma 4.1 are used to restrict two SL-fragments (to be composed for S-region) to have all sync rules and transitions that are necessary for synchronizing L-fragments in $\varvec{\varGamma}$. We can prove that the three conditions are necessary as follows.

• For the second condition Consider a transition with a sync rule. Based on the inference rule 3.3 for the synchronization composition defined in Definition 3.9, every sync rule that is used to synchronize between two lifecycles, those transitions, and states related to the sync rule will be included in the synchronized product. So, if a sync rule is used to synchronize $\ell^{{\varvec{C}_{\varvec{i}} }}$ with any L-fragment that is not in $\varGamma$, then a transition and its related states of such L-fragment will be included in the composition result. This clearly means that there will exist a transition from/to a state that does not belong to any L-fragment in $\varGamma$; therefore, the result fragment does not satisfy the condition of AL-fragment.

• For the third and fourth conditions The third condition is used to restrict all the entry transitions of one fragment to be synchronized with all the entry transitions of another fragment to be composed. Similarly, the third condition is for the exit transitions. Consider an entry or exit transition with a sync rule. Assume two synchronized L-fragments with multiple entry transitions and there exists an entry transition in one fragment that does not synchronize with any entry transition of another fragment. Based on the inference rule (3.3) in Definition 3.9, the composed entry transition in the synchronized product derived from that transition will never fire since no sync rule is induced on it; therefore, the goal-reachability of the composed fragment is violated. The same problem also occurs in the case of having an exit transition of one fragment without a sync rule on the exit transition of another fragment to be composed. Therefore, the soundness cannot be guaranteed without these two conditions.

This completes the proof of Lemma 4.1.$\hfill\square$

Proof of Lemma 4.2

We can prove it by construction using the ex-lifecycle condition (in Definition 4.11), the B-consistency condition (in Definition 4.2), the condition for atomic composition of SL-fragments (in Lemma 4.1), and the condition of B-consistent refined L-fragment (in Theorem 4.1) to show that if the conditions of Lemma 4.2 hold, $\ell$ is B-consistent with ${\mathcal{L}}_{Y}^{{\prime }} \otimes \ell$. Revisiting the four conditions in Lemma 4.1, the composition of two SL-fragments is considered as a composite AL-fragment in the synchronized product if the SL-fragments are AL-fragment and the sync rules of entry/exit transitions of one fragment completely synchronize the entry/exit transitions of another fragment. Here in Lemma 4.2, the AL-fragment condition conforms to the first condition of Lemma 4.1 and the ex-lifecycle condition (in Definition 4.11) conforms to the second, third, and fourth conditions of the Lemma 4.1. Followed from Theorem 4.1, the composed lifecycle can be considered as a refined, composite AL-fragment (composed of ${\mathcal{L}^{\prime}}_{{C_{y} }}$ and $\ell$) in $\ell$; therefore, the composed lifecycle is B-consistent with $\ell$.$\hfill \square$

Proof of Lemma 4.3

Similar to the proof of Lemma 4.2, we can prove it by construction using Definition 4.12, the B-consistency condition (in Definition 4.2), the condition for the atomic composition of SL-fragments (in Lemma 4.1), and the condition of B-consistent refined L-fragment (in Theorem 4.1). This proof can be achieved based on the proof of Lemma 4.1. If the composition of two synchronized fragments in the refined S-region is atomic, then based on Theorem 4.1 (by considering refined S-region as a refined L-fragment), the B-consistency is preserved. $\hfill \square$

Proof of Lemma 4.4

The proof can be derived from Lemmas 4.2 and 4.3 as the refinement of an existing artifact satisfies the condition of Lemma 4.3 and the artifact extension satisfies the condition of Lemma 4.2.$\hfill\square$

Proof of Lemma 4.5

The proof can be derived from Lemma 4.4 and Definition 4.13 by taking into account the transitivity property of sync rules and the lifecycle composition (in Definition 3.9).$\hfill\square$

Proof of Lemma 4.6

We can prove it by construction using Definitions 4.14, 4.15, 4.16, the B-consistency condition (in Definition 4.2), and the condition for the atomic composition of SL-fragments (in Lemma 4.1) to show that if the conditions of Lemma 4.6 holds, the lifecycle composition of every transition in $T^{re}$ is B-consistent with the lifecycle composition of every L-fragment in $L^{re}$ and ${\mathcal{L}}_{Y}$. For every reducible L-fragments in $L^{re}$, it is reduced into a transition. Based on Definitions 4.14, 4.15, and Lemma 4.1, the composition of reducible L-fragments (with corresponding reduced sync rules) can be considered as a composite AL-fragment; therefore, can be reduced without violating the B-consistency condition.$\hfill\square$

Proof of Theorem 4.1

The theorem can be proved by checking: for each statement of the theorem, a refined L-fragment (in Definition 4.5) does not violate the B-consistency condition (in Definition 4.2).

• Consider the first statement of the theorem. An AL-fragment that refines a base lifecycle always preserves the B-consistency condition as the AL-fragment is atomic and it has a single-entry state and a single exit state. An entire lifecycle of the L-fragment can be completely reduced (or abstracted) in a single transition if such L-fragment is atomic, i.e., being an AL-fragment. We can see that the condition of AL-fragment (in Definition 4.5) naturally conforms to Conditions 4.1 and 4.2 of the B-consistency (Definition 4.2)

• Consider the second statement of the theorem. We can see that the condition of this statement restricts a refined L-fragment to be completely encapsulated within a single state. For every L-occurrence of the L-fragment, it must be originated from a transition fired from an outside state (not in the L-fragment) and must reach to a transition fired to another outside state. We can see that the condition for substituting a state with a refined L-fragment conforms to Condition 4.3 of the B-consistency (Definition 4.2).

This completes the proof of Theorem 4.1.$\hfill\square$

Proof of Theorem 4.2

The theorem can be proved by construction using the three inference rules for lifecycle composition (in Definition 3.9), the soundness condition (in Definition 3.11), and the B-consistency condition (in Definition 4.2). As refined L-fragments do no introduce any synchronization dependencies to specialized artifacts, then the proof follows that the composed lifecycle is always sound. As the conditions of Theorem 4.1 restrict a specialized artifact preserves the B-consistency when applying refined L-fragments, the lifecycle composition of every specialized artifact is B-consistent.$\hfill \square$

Proof of Theorem 4.3

We can prove the theorem as follows.

• For the if condition, we must prove that if the two statements are satisfied, then $\Pi^{{\prime }}$ is B-consistent with $\Pi$. For the first condition, we prove that each specialized artifact needs to be B-consistent with its base artifact. Based on Definition 4.4, this statement follows from Theorem 4.2. For the second condition, we prove that why each sync specialization needs to be S-consistent. Based on Definition 4.18, this statement follows from Lemmas 4.2, 4.3, 4.5, and 4.6. As each of Lemmas has the condition to preserve the B-consistency for each method of sync specialization (extension, refinement, and reduction), therefore, the second statement holds.

This completes the proof of the if direction.

• For the only if condition we must prove that the two statements satisfy if $\Pi^{{\prime }}$ is a behavior-consistent specialization of $\Pi$. This can be proved based on the definition of ACP Specialization (in Definition 4.1) and the definition of lifecycle specialization B-consistency (in Definition 4.4), and S-consistency (Definition 4.18). In ACP Specialization, we define the three specialization methods: artifact extension, refinement, and reduction. First, the lifecycle B-consistency of each specialized artifact must hold as it follows from Theorem 4.2. Then, consider the three S-consistency conditions based on artifact all these specialization methods.

• For artifact extension A newly added artifact is not needed to be B-consistent. Either Lemma 4.2 (sync extension) or Lemma 4.5 (sync refinement of existing and extended artifacts), or the combination of them is required.

• For artifact refinement If there is no synchronization considered, the B-consistency for artifact refinement follows from Theorem 4.2. With synchronization, Theorem 4.2 and Lemma 4.3 (sync refinement) are required.

• For artifact reduction A removed artifact is not needed to be B-consistent. But the existing artifact with reduced lifecycle must be B-consistent and it follows from Theorem 4.2 and Lemma 4.6 (sync reduction).

This completes the proof of the only if direction.

Therefore, the proof of Theorem 4.3 is complete.$\hfill\square$