scholarly journals A Comparison of Petri Net Semantics under the Collective Token Philosophy

1998 ◽  
Vol 5 (17) ◽  
Author(s):  
Roberto Bruni ◽  
José Meseguer ◽  
Ugo Montanari ◽  
Vladimiro Sassone
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Equational Logic ◽  
Monoidal Categories ◽  
Transition Systems ◽  
Logical Description ◽  
Membership Equational Logic

In recent years, several semantics for place/transition Petri nets have been proposed that adopt the collective token philosophy. We investigate distinctions and similarities between three such models, namely configuration structures, concurrent transition systems, and (strictly) symmetric (strict) monoidal categories. We use the notion of adjunction to express each connection. We also present a purely logical description of the collective token interpretation of net behaviours in terms of theories and theory morphisms in partial membership equational logic.

Target-oriented Petri Net Synthesis

2020 ◽  
Author(s):  
Eike Best ◽  
Raymond Devillers ◽  
Evgeny Erofeev ◽  
Harro Wimmel
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Transition System ◽  
Efficient Synthesis ◽  
Transition Systems ◽  
Np Complete ◽  
Full Class ◽  
Petri Net Synthesis ◽  
Labelled Transition System ◽  
Additional Constraints

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

Target-oriented Petri Net Synthesis

2020 ◽  
Vol 175 (1-4) ◽  
pp. 97-122
Author(s):  
Eike Best ◽  
Raymond Devillers ◽  
Evgeny Erofeev ◽  
Harro Wimmel
Keyword(s):  
Petri Nets ◽  
Circuit Design ◽  
Petri Net ◽  
Transition System ◽  
Transition Systems ◽  
Np Complete ◽  
Full Class ◽  
Petri Net Synthesis ◽  
Labelled Transition System ◽  
Additional Constraints

When a Petri net is synthesised from a labelled transition system, it is frequently desirable that certain additional constraints are fulfilled. For example, in circuit design, one is often interested in constructing safe Petri nets. Targeting such subclasses of Petri nets is not necessarily computationally more efficient than targeting the whole class. For example, targeting safe nets is known to be NP-complete while targeting the full class of place/transition nets is polynomial, in the size of the transition system. In this paper, several classes of Petri nets are examined, and their suitability for being targeted through efficient synthesis from labelled transition systems is studied and assessed. The focus is on choice-free Petri nets and some of their subclasses. It is described how they can be synthesised efficiently from persistent transition systems, summarising and streamlining in tutorial style some of the authors’ and their groups’ work over the past few years.

scholarly journals Strong Concatenable Processes: An Approach to the Category of Petri Net Computations

1994 ◽  
Vol 1 (33) ◽  
Author(s):  
Vladimiro Sassone
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Monoidal Categories ◽  
Commutative Monoids ◽  
Precise Sense ◽  
Abstract Description ◽  
Symmetric Monoidal Categories

We introduce the notion of <em>strong concatenable process</em> for Petri nets as the least refinement of non-sequential (concatenable) processes which can be expressed abstractly by means of a <em> functor</em> Q[_] from the category of Petri nets to an appropriate category of symmetric strict monoidal categories with free non-commutative monoids of objects, in the precise sense that, for each net N, the strong concatenable processes of N are isomorphic to the arrows of Q[N]. This yields an axiomatization of the causal behaviour of Petri nets in terms of symmetric strict monoidal categories.<br /> <br />In addition, we identify a <em>coreflection</em> right adjoint to Q[_] and we characterize its replete image in the category of symmetric monoidal categories, thus yielding an abstract description of the category of net computations.

PETRI NETS AND STEP TRANSITION SYSTEMS

1992 ◽  
Vol 03 (04) ◽  
pp. 443-478 ◽  
Author(s):  
MADHAVAN MUKUND
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Transition System ◽  
Computing Systems ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Natural Sense ◽  
Step Transition ◽  
Operational Behaviour ◽  
Natural Way

Labelled transition systems are a simple yet powerful formalism for describing the operational behaviour of computing systems. They can be extended to model concurrency faithfully by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step. Petri nets (or Place/Transition nets) give rise to such step transition systems in a natural way—the marking diagram of a Petri net is the canonical transition system associated with it. In this paper, we characterize the class of PN-transition systems, which are precisely those step transition systems generated by Petri nets. We express the correspondence between PN-transition systems and Petri nets in terms of an adjunction between a category of PN-transition systems and a category of Petri nets in which the associated morphisms are behaviour-preserving in a strong and natural sense.

scholarly journals An axiomatization of the category of Petri net computations

1998 ◽  
Vol 8 (2) ◽  
pp. 117-151 ◽  
Author(s):  
VLADIMIRO SASSONE
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Monoidal Categories ◽  
Precise Sense

We introduce the notion of strongly concatenable process as a refinement of concatenable processes (Degano et al. 1996), which can be expressed axiomatically via a functor [Qscr ](_) from the category of Petri nets to an appropriate category of symmetric strict monoidal categories, in the precise sense that, for each net N, the strongly concatenable processes of N are isomorphic to the arrows of [Qscr ](N). In addition, we identify a coreflection right adjoint to [Qscr ](_) and characterize its replete image, thus yielding an axiomatization of the category of net computations.

scholarly journals Articulations and Products of Transition Systems and their Applications to Petri Net Synthesis

2022 ◽  
Vol 183 (1-2) ◽  
pp. 1-31
Author(s):  
Raymond Devillers
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Composition Operators ◽  
Original System ◽  
Divide And Conquer ◽  
Transition Systems ◽  
Structure Transition ◽  
Labelled Transition Systems ◽  
Speed Up ◽  
Petri Net Synthesis

In order to speed up the synthesis of Petri nets from labelled transition systems, a divide and conquer strategy consists in defining decompositions of labelled transition systems, such that each component is synthesisable iff so is the original system. Then corresponding Petri Net composition operators are searched to combine the solutions of the various components into a solution of the original system. The paper presents two such techniques, which may be combined: products and articulations. They may also be used to structure transition systems, and to analyse the performance of synthesis techniques when applied to such structures.

Constrained Petri Nets. Part II: Generalizations and extensions

1983 ◽  
Vol 6 (3-4) ◽  
pp. 333-374
Author(s):  
H.J.M. Goeman ◽  
L.P.J. Groenewegen ◽  
H.C.M. Kleijn ◽  
G. Rozenberg
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Theoretical Framework ◽  
General Constraints ◽  
Context Free ◽  
Boolean Expressions

This paper continues the investigation froll1 [Goeman et al.] concerning the use of sets of places of a Petri net as additional (to input places) constraints for granting concession. Now interpretations of more general constraints are considered and expressed as Boolean expressions. This gives rise to various classes of constrained Petri nets. These are compared in the language theoretical framework introduced in [Goeman et al.]. An upperbound for the language defining power is found in the class of context-free programmed languages.

An Axiomatic Characterization of a Class of Petri Nets

1991 ◽  
Vol 14 (4) ◽  
pp. 477-491
Author(s):  
Waldemar Korczynski
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Axiomatic Characterization ◽  
Algebraic Characterization

In this paper an algebraic characterization of a class of Petri nets is given. The nets are characterized by a kind of algebras, which can be considered as a generalization of the concept of the case graph of a (marked) Petri net.

The Quantitative Assessment of Domino Effects Based on Stochastic Petri Nets

2008 ◽  
Vol 44-46 ◽  
pp. 537-544
Author(s):  
Shi Yi Bao ◽  
Jian Xin Zhu ◽  
Li J. Wang ◽  
Ning Jiang ◽  
Zeng Liang Gao
Keyword(s):  
Petri Nets ◽  
State Space ◽  
Petri Net ◽  
Quantitative Assessment ◽  
Stochastic Petri Nets ◽  
Industrial Park ◽  
Domino Effect ◽  
State Space Explosion ◽  
Stochastic Petri Net ◽  
Chemical Industrial Park

The quantitative analysis of “domino” effects is one of the main aspects of hazard assessment in chemical industrial park. This paper demonstrates the application of heterogeneous stochastic Petri net modeling techniques to the quantitative assessment of the probabilities of domino effects of major accidents in chemical industrial park. First, five events are included in the domino effect models of major accidents: pool fire, explosion, boiling liquid expanding vapour explosion (BLEVE) giving rise to a fragment, jet fire and delayed explosion of a vapour cloud. Then, the domino effect models are converted into Generalized Stochastic Petri net (GSPN) in which the probability of the domino effect is calculated automatically. The Stochastic Petri nets’ models, which are state-space based ones, increase the modeling flexibility but create the state-space explosion problems. Finally, in order to alleviate the state-space explosion problems of GSPN models, this paper employs Stochastic Wellformed Net (SWN), a particular class of High-Level (colored) SPN. To conduct a case study on a chemical industrial park, the probability of domino effects of major accidents is calculated by using the GSPN model and SWN model in this paper.

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