Synchrony vs. Causality in Asynchronous Petri Nets

Given a synchronous system, we study the question whether the behaviour of that system can be exhibited by a (non-trivially) distributed and hence asynchronous implementation. In this paper we show, by counterexample, that synchronous systems cannot in general be implemented in an asynchronous fashion without either introducing an infinite implementation or changing the causal structure of the system behaviour.

💡 Research Summary

The paper investigates whether the behavior of a synchronous system can be faithfully reproduced by a distributed, asynchronous implementation, using Petri nets as the formal model. After introducing the basic notions of Petri nets—places, transitions, flow relations, labeling, and markings—the authors focus on 1‑safe nets, where each place can hold at most one token.

A key concept is “distributability”: a net is distributable if there exists a mapping of its elements to physical locations such that every transition and all its pre‑places reside on the same location, while concurrently executable transitions must be placed on distinct locations. This leads to Observation 1, which states that any sequence of transitions forming a chain of conflicts (t₀ ⌣ tₙ with non‑overlapping pre‑places) prevents distributability.

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