Compositionality of Systems and Partially Ordered Runs
🤖 AI Summary
This work investigates the formal composition and decomposition of partially ordered runs in distributed systems while preserving semantic consistency. To this end, we develop a unified framework that tightly integrates Petri nets with their associated partially ordered event structures—i.e., runs. Within this framework, we rigorously prove that the set of runs of a composed Petri net is precisely the composition of the runs of its constituent subnets, thereby establishing a compositional principle at the level of runs. This result not only ensures semantic alignment between Petri nets and their runs under composition and decomposition operations but also provides a solid theoretical foundation for modular modeling and verification of distributed systems.
Application Category
📝 Abstract
In the late 1970s, C.A. Petri introduced partially ordered event occurrences (runs), then called \emph{processes}, as the appropriate model to describe the individual evolutions of distributed systems. Here, we present a unified framework for handling Petri nets and their runs, specifically to compose and decompose them. It is shown that, for nets $M$ and $N$, the set of runs of the composed net $M \bullet N$ equals the composition of the runs of $M$ and $N$.
Problem
Research questions and friction points this paper is trying to address.
Compositionality
Partially Ordered Runs
Petri Nets
Distributed Systems
Process Models
Innovation
Methods, ideas, or system contributions that make the work stand out.
Compositionality
Partially Ordered Runs
Petri Nets
Distributed Systems
Process Composition
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