[Paper Review] Dynamic Causality in Event Structures (Technical Report)

Youssef Arbach, David Karcher+2 more|arXiv (Cornell University)|Apr 2, 2015

Business Process Modeling and Analysis2 references5 citations

TL;DR

This technical report introduces Dynamic Causality in Event Structures (DCES), extending Prime Event Structures with mechanisms to dynamically add or remove causal dependencies between events. It proves that DCESs are strictly more expressive than Existing Bundle Event Structures (EBESs), as shown by a counterexample where disjunctive causality cannot be captured in EBESs, demonstrating the necessity of dynamic causality for modeling certain concurrent behaviors.

ABSTRACT

In [1] we present an extension of Prime Event Structures by a mechanism to express dynamicity in the causal relation. More precisely we add the possibility that the occurrence of an event can add or remove causal dependencies between events and analyse the expressive power of the resulting Event Structures w.r.t. to some well-known Event Structures from the literature. This technical report contains some additional information and the missing proofs of [1].

Motivation & Objective

• To extend Prime Event Structures with dynamic causal dependencies that can be added or removed during execution.
• To formally analyze the expressive power of the resulting Dynamic Causality in Event Structures (DCES) framework.
• To compare DCES with existing models like EBES and SES, showing limitations in capturing certain concurrent behaviors.
• To prove that DCESs are strictly more expressive than EBESs using formal embeddings and counterexamples.
• To provide missing proofs and additional technical details for the main results in the companion paper [1].

Proposed method

• Extends Prime Event Structures with a dynamic causality mechanism allowing causal dependencies to be created or deleted based on event occurrences.
• Introduces the concept of transition-based configurations and defines transition equivalence between models to compare expressive power.
• Defines an embedding function `rces(μ)` that maps transition-based event structures to Resolvable Conflict Event Structures (RCES), preserving transitions.
• Uses trace-based configurations in Sequential Event Structures (SES) to show equivalence between traced and transition-based semantics.
• Applies a formal embedding `dces(ξ)` from EBES to DCES, proving that every EBES configuration is preserved in the DCES model.
• Employs counterexamples (e.g., `σ_ξ`) to demonstrate that certain configurations involving disjunctive causality cannot be modeled in EBES, proving strict expressiveness increase.

Experimental results

Research questions

• RQ1 Can dynamic causal dependencies—created or removed by event occurrences—be formally integrated into event structure models?
• RQ2 How does the expressive power of DCES compare to that of EBES and SES models?
• RQ3 Is there a configuration that can be modeled in DCES but not in EBES?
• RQ4 Can transition-based and trace-based semantics be shown to coincide in certain classes of event structures?
• RQ5 What is the formal relationship between EBES and DCES in terms of configuration preservation and causal structure?

Key findings

• DCESs are strictly more expressive than EBESs, as demonstrated by a counterexample involving disjunctive causality that cannot be captured in EBES.
• The embedding `rces(μ)` preserves transition behavior and results in a valid RCES, proving transition equivalence between the original and embedded models.
• In SESs, trace-based and transition-based configurations are equivalent, validating the use of either semantics in this class.
• The embedding `dces(ξ)` from EBES to DCES preserves all configurations, showing that every EBES configuration is realizable in the corresponding DCES.
• The partial order of causal dependencies in a configuration is preserved under the `dces` embedding, ensuring structural fidelity.
• The existence of a DCES configuration without a corresponding EBES model proves that dynamic causality is essential for modeling certain concurrent behaviors.