[Paper Review] Compositional Conformance Checking of Nested Petri Nets and Event Logs of Multi-Agent Systems

Khalil Mecheraoui, Julio C. Carrasquel+1 more|arXiv (Cornell University)|Mar 16, 2020

Business Process Modeling and Analysis13 references4 citations

TL;DR

This paper proposes a compositional conformance checking approach for nested Petri nets and event logs in multi-agent systems by projecting event logs onto model components (system net and agent nets), enabling independent conformance checks. The key contribution is a formal proof that an event log perfectly fits a nested Petri net if and only if it is syntactically correct and each component projection perfectly fits its corresponding model component, ensuring correctness and component-specific diagnostics without artificial decomposition boundaries.

ABSTRACT

This paper presents a compositional conformance checking approach between nested Petri nets and event logs of multi-agent systems. By projecting an event log onto model components, one can perform conformance checking between each projected log and the corresponding component. We formally demonstrate the validity of our approach proving that, to check fitness of a nested Petri net is equivalent to check fitness of each of its components. Leveraging the multi-agent system structure of nested Petri nets, this approach may provide specific conformance diagnostics for each system component as well as to avoid to compute artificial boundaries when decomposing a model for conformance checking.

Motivation & Objective

• To address the challenge of conformance checking in large, complex multi-agent systems with high concurrency.
• To overcome limitations of existing conformance checking methods that rely on artificial decomposition and lack component-specific diagnostics.
• To leverage the natural modularity of nested Petri nets to enable compositional verification of event logs.
• To formally establish the equivalence between global fitness and component-wise fitness in nested Petri net models.
• To provide a foundation for precise, component-level conformance diagnostics in multi-agent system process mining.

Proposed method

• Project an event log of a multi-agent system onto the system net and each agent net (net token) to obtain component-specific projections.
• Define syntactic correctness of an event log with respect to a nested Petri net using trace alignment and binding consistency.
• Formally define 'perfect fit' of a log projection to a model component as the existence of a valid run in the component's Petri net.
• Use a formal model of nested Petri nets where tokens can be Petri nets, representing agents with internal behavior.
• Establish equivalence between global log fitting and component-wise fitting through a formal theorem and proof.
• Apply standard conformance checking techniques (e.g., replay, alignment) independently to each component projection.

Experimental results

Research questions

• RQ1 Can conformance checking be effectively decomposed in nested Petri nets without introducing artificial boundaries?
• RQ2 Is the fitness of a global event log equivalent to the fitness of its projections on individual model components?
• RQ3 Can component-specific conformance diagnostics be reliably derived from log projections in multi-agent systems?
• RQ4 Does the compositional approach preserve the correctness of global conformance checking?
• RQ5 How can nested Petri nets be used to model multi-agent systems in a way that naturally supports compositional verification?

Key findings

• An event log perfectly fits a nested Petri net if and only if it is syntactically correct with respect to the model and each component projection perfectly fits its corresponding model component.
• The compositional approach ensures correctness by preserving the global fitness property through local checks on system net and agent net components.
• The method avoids artificial decomposition by leveraging the inherent modularity of nested Petri nets, where each net token represents a real agent.
• Component-specific diagnostics are naturally supported, as each projection can be analyzed independently for conformance issues.
• The approach is formally validated through a rigorous proof of the equivalence theorem, establishing theoretical soundness.
• The framework enables scalable and precise conformance checking in complex, concurrent multi-agent systems.