Constructing Complete Finite Prefixes of Symbolic Unfoldings for Safe High-level Petri Nets

Concetti Chiave

The authors generalize the concept of complete finite prefixes and the ERV-algorithm from low-level Petri nets to the symbolic unfoldings of a class of safe high-level Petri nets, where the guards are expressed in a decidable theory and the nets have finitely many reachable markings.

Sintesi

The paper starts by recalling the definitions and formalism for high-level Petri nets and symbolic unfoldings from prior work. It then defines the class of safe high-level Petri nets, called NF, for which the authors generalize the construction of complete finite prefixes.
The key contributions are:

Lifting the concepts of completeness, adequate orders, and cut-off events to the level of symbolic unfoldings of high-level Petri nets. The authors show that for P/T nets interpreted as high-level nets, the generalized concepts coincide with their low-level counterparts.

Generalizing the ERV-algorithm to construct small complete finite prefixes of the symbolic unfoldings of high-level Petri nets in NF.

Identifying a more general class of "symbolically compact" high-level Petri nets, where the number of steps needed to reach all reachable markings is bounded, but the number of reachable markings may be infinite. The authors adapt the generalized ERV-algorithm to handle this class.

Presenting a prototype implementation of the generalized ERV-algorithm and evaluating it on four new benchmark families of high-level Petri nets.

Statistiche

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Citazioni

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Approfondimenti chiave tratti da

Taking Complete Finite Prefixes To High Level, Symbolically

by Nick... alle arxiv.org 04-10-2024

https://arxiv.org/pdf/2311.11443.pdf

Domande più approfondite

How can the generalized ERV-algorithm be further extended to handle high-level Petri nets that are not necessarily safe

To extend the generalized ERV-algorithm to handle high-level Petri nets that are not necessarily safe, we need to consider the additional complexities introduced by unsafe nets. One approach could be to modify the algorithm to accommodate multiple tokens in a single place, which is a characteristic of unsafe nets. This would involve adjusting the predicates and constraints used in the algorithm to account for the potential presence of multiple tokens in a place. Additionally, the algorithm may need to incorporate more sophisticated checks and conditions to ensure the correctness of the unfolding process for unsafe nets. By adapting the algorithm to handle the unique characteristics of unsafe high-level Petri nets, we can extend its applicability to a broader range of models.

What are the theoretical limits of the symbolic unfolding approach compared to directly constructing the unfolding of the expanded low-level Petri net

The theoretical limits of the symbolic unfolding approach compared to directly constructing the unfolding of the expanded low-level Petri net lie in the complexity and expressiveness of the high-level formalism. While symbolic unfolding offers a more concise representation of the net's behavior, it may not always capture all the intricate details present in the low-level unfolding. The symbolic approach is advantageous in terms of readability and analysis, but it may lack the granularity required for certain intricate scenarios. In cases where the high-level representation introduces additional complexities or ambiguities, directly constructing the low-level unfolding may provide a more detailed and accurate depiction of the system's behavior. The symbolic approach excels in scenarios where a high-level overview suffices, but it may struggle with highly detailed or complex systems that demand a more granular representation.

Can the symbolic approach always outperform the low-level one

Beyond the classes of high-level Petri nets considered in the work, there may be other classes for which complete finite prefixes of the symbolic unfolding can be efficiently constructed. One potential class to explore could be high-level Petri nets with specific structural constraints or behavioral patterns that lend themselves well to the symbolic unfolding approach. For example, nets with certain symmetry properties, regular structures, or well-defined behavioral characteristics may allow for efficient construction of complete finite prefixes. By identifying and analyzing the structural and behavioral properties of different classes of high-level Petri nets, it may be possible to determine additional classes for which the symbolic unfolding methodology can be effectively applied to construct complete finite prefixes.