Using Transition Invariants for Reachability Analysis of Petri Nets

Kostin, Alexander

doi:10.5772/5328

Cited by 6 publications

(5 citation statements)

References 23 publications

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“…Then, one can apply an efficient enumeration scheme to find all the relevant FCVs, based on the following two features: i) an ILP formulation to characterize the admissible FCVs of maximum length K, and ii) a Branch & Bound (B&B) procedure that partitions the solution space once a solution is found, introducing suitable constraints to exclude previously found solutions. Notice that, differently from the approach of [25], where the existence of fireable TSs compatible with the calculated FCVs is verified a posteriori, here the admissibility check is integrated in the enumeration procedure, to avoid carrying over useless FCVs to the -more costly-timed analysis.…”

Section: A Finiteness Of the Fcvsmentioning

confidence: 99%

“…The set of vectors y = Consider e.g. the PN system depicted in Figure 2 [25], for which we want to solve the reachability problem from m 0 = 2p 1 to m t = 2p 1 +p 9 with K = 25. The set of MS T-invariants of the complemented net is given by Y ms = {y 1 , y 2 , y 3 }, where y 1 = [0 0 1 1 1 0 1 0 0 0 0] T , y 2 = [1 1 0 0 0 1 1 0 0 0 0] T , and y 3 = [0 0 0 0 0 0 0 1 1 1 1] T .…”

Section: B An Ilp Formulation To Characterize Admissible Fcvsmentioning

confidence: 99%

“…(t 3 t 1 t 2 t 7 t 1 t 2 t 4 t 9 t 5 t 8 t 10 t 7 t 7 t 6 t 6 ). In other words, to reach m t one has to follow σ 3 , but in order to enable the sequence the necessary tokens must be borrowed through suitable executions of the T-invariants of the original PN [25].…”

Section: B An Ilp Formulation To Characterize Admissible Fcvsmentioning

confidence: 99%

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Supervisory Control of Timed Discrete-Event Systems With Logical and Temporal Specifications

Basile

Cordone²,

Piroddi

2022

IEEE Trans. Automat. Contr.

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A novel framework is introduced for the supervisory control (SC) of timed discrete event systems, based on Time Petri nets. The method encompasses both logical (markings to reach or avoid) and temporal specifications (arrival and departure times in specific markings). It relies on the construction of a partial forward reachability graph of the Modified State Class Graph type and the formulation of integer linear programming problems to establish suitable firing time intervals (FTIs) for the controllable transitions. The SC algorithm provides for each enabled controllable transition the largest FTI that guarantees that the specifications are met, irrespectively of the firing times of the uncontrollable transitions.

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Section: A Finiteness Of the Fcvsmentioning

confidence: 99%

Section: B An Ilp Formulation To Characterize Admissible Fcvsmentioning

confidence: 99%

See 1 more Smart Citation

Supervisory Control of Timed Discrete-Event Systems With Logical and Temporal Specifications

Basile

Cordone²,

Piroddi

2022

IEEE Trans. Automat. Contr.

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show abstract

“…A PN is a mathematical model for representation and analysis of concurrent processes [18]. The problem of whether some arbitrary state is reachable from a fixed initial state of a PN is of basic importance in the field of computer science [19][20][21][22][23][24][25]. PNs enable modeling in a multi-modal way, ranging from semi-quantitative to detailed quantitative modeling.…”

Section: Introductionmentioning

confidence: 99%

Holistic View on the Structure of Immune Response: Petri Net Model

et al. 2023

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The simulation of immune response is a challenging task because quantitative data are scarce. Quantitative theoretical models either focus on specific cell–cell interactions or have to make assumptions about parameters. The broad variation of, e.g., the dimensions and abundance between lymph nodes as well as between individual patients hampers conclusive quantitative modeling. No theoretical model has been established representing a consensus on the set of major cellular processes involved in the immune response. In this paper, we apply the Petri net formalism to construct a semi-quantitative mathematical model of the lymph nodes. The model covers the major cellular processes of immune response and fulfills the formal requirements of Petri net models. The intention is to develop a model taking into account the viewpoints of experienced pathologists and computer scientists in the field of systems biology. In order to verify formal requirements, we discuss invariant properties and apply the asynchronous firing rule of a place/transition net. Twenty-five transition invariants cover the model, and each is assigned to a functional mode of the immune response. In simulations, the Petri net model describes the dynamic modes of the immune response, its adaption to antigens, and its loss of memory.

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“…Reference [5] mainly analyzes the correctness in Web service composition. Reference [6][7] analyzes the accessibility of the web by T-invariant. The existed modeling methods is not perfect.…”

Section: Introductionmentioning

confidence: 99%

The Modeling Method and Analysis of Online Top-Up System Based on Open Petri Net

Fang

2014

AMM

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Petri nets have structure and behavior properties, it is convenient to analyze some complex system based on its mathematical analysis methods. Online top-up system is an open network system. The modeling method of this system based on general Petri net has some limitations. A new modeling method based on open Petri net to study online top-up system is proposed, and analyze the open Petri net model by T-invariant. This method laid a foundation for the study of open online top-up system.

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Using Transition Invariants for Reachability Analysis of Petri Nets

Cited by 6 publications

References 23 publications

Supervisory Control of Timed Discrete-Event Systems With Logical and Temporal Specifications

Supervisory Control of Timed Discrete-Event Systems With Logical and Temporal Specifications

Holistic View on the Structure of Immune Response: Petri Net Model

The Modeling Method and Analysis of Online Top-Up System Based on Open Petri Net

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