scholarly journals Transition System Models for Concurrency

1992 ◽  
Vol 21 (399) ◽  
Author(s):  
Madhavan Mukund
Keyword(s):  
Petri Nets ◽  
Transition System ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
System Models ◽  
Elementary Transition ◽  
Step Transition ◽  
Sequential Behaviour

<p>Labelled transition systems can be extended to faithfully model concurrency by permitting transitions between states to be labelled by a collection of actions, denoting a concurrent step, We can characterize a subclass of these <em>step transition systems</em>, called PN-transition systems, which describe the behaviour of Petri nets.</p><p>This correspondence is formally described in terms of a coreflection between a category of <em>PN</em>-transition systems and a category of Petri nets.</p><p>In this paper, we show that we can define subcategories of <em>PN</em>-transition systems whose objects are <em> safe PN-transition systems and elementary PN-transition systems</em> such that there is a coreflection between these subcategories and subcategories of our category of Petri nets corresponding to safe nets and elementary net systems.</p><p>We also prove that our category of elementary <em>PN</em>-transition systems is equivalent to the category of (sequential) <em> elementary transition systems</em> defined by Nielsen, Rozenberg and Thiagarajan, thereby establishing that the concurrent behaviour of an elementary net system can be completely recovered from a description of its sequential behaviour. Finally, we establish a coreflection between our category of safe <em>PN</em>-transition system and a subcategory of <em>asynchronous transition systems</em> which has been shown by Winskel and Nielsen to be closely linked to safe nets.</p>

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.

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.

scholarly journals Model Checking Coloured Petri Nets - Exploiting Strongly Connected Components

1997 ◽  
Vol 26 (519) ◽  
Author(s):  
Allan Cheng ◽  
Søren Christensen ◽  
Kjeld Høyer Mortensen
Keyword(s):  
Model Checking ◽  
Petri Nets ◽  
The State ◽  
Connected Components ◽  
Coloured Petri Nets ◽  
Transition Systems ◽  
Strongly Connected Components ◽  
State Spaces ◽  
Labelled Transition Systems ◽  
Strongly Connected

In this paper we present a CTL-like logic which is interpreted over the state spaces of Coloured Petri Nets. The logic has been designed to express properties of both state and transition information. This is possible because the state spaces are labelled transition systems. We compare the expressiveness of our logic with CTL's. Then, we present a model checking algorithm which for efficiency reasons utilises strongly connected components and formula reduction rules. We present empirical results for non-trivial examples and compare the performance of our algorithm with that of Clarke, Emerson, and Sistla.

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 Who is obliged when many are involved? Labelled transition system modelling of how obligation arises

2020 ◽  
Author(s):  
Piotr Kulicki ◽  
Robert Trypuz ◽  
Marek Sergot
Keyword(s):  
Freedom Of Expression ◽  
Transition System ◽  
The Other ◽  
System Modelling ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Polish Law ◽  
The Right ◽  
Labelled Transition System

AbstractThe paper tackles the problem of the relation between rights and obligations. Two examples of situations in which such a relation occurs are discussed. One concerns the abortion regulations in Polish law, the other one—a clash between freedom of expression and freedom of enterprise occurring in the context of discrimination. The examples are analysed and formalised using labelled transition systems in the $$n\mathcal {C}+$$ n C + framework. Rights are introduced to the system as procedures allowing for their fulfilment. Obligations are based on the requirement of cooperation in the realisation of the goals of the agent that has a right. If the right of an agent cannot be fulfilled without an action of another agent, then that action is obligatory for that agent. If there are many potential contributors who are individually allowed to refuse, then the last of them is obliged to help when all the others have already refused. By means of formalisation this account of the relation under consideration is precisely expressed and shown consistent.

scholarly journals On the Power of Labels in Transition Systems

2001 ◽  
Vol 8 (19) ◽  
Author(s):  
Jirí Srba
Keyword(s):  
Model Checking ◽  
Petri Nets ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Pushdown Automata ◽  
General Reduction

In this paper we discuss the role of labels in transition systems with regard to bisimilarity and model checking problems. We suggest a general reduction from labelled transition systems to unlabelled ones, preserving bisimilarity and satisfiability of mu-calculus formulas. We apply the reduction to the class of transition systems generated by Petri nets and pushdown automata, and obtain several decidability/complexity corollaries for unlabelled systems. Probably the most interesting result is undecidability of strong bisimilarity for unlabelled Petri nets.

scholarly journals Elementary Transition Systems and Refinement

1991 ◽  
Vol 20 (346) ◽  
Author(s):  
Mogens Nielsen ◽  
Grzegorz Rozenberg ◽  
P. S. Thiagarajan
Keyword(s):  
Transition System ◽  
Local State ◽  
Transition Systems ◽  
Natural Properties ◽  
Elementary Transition ◽  
Abstract Level ◽  
Standard Notion ◽  
Definition Of ◽  
Simple Notion

The model of Elementary Transition Systems has been introduced by the authors as an abstraction of Elementary Net Systems - with a formal embedding in terms of a categorical coreflection, keeping behavioural information like causality, concurrency and conflict, but forgetting the concrete programming of a particular behaviour over an event set using conditions. In this paper we give one example of the advantages of ETS over ENS, - the definition of local state refinement. We show that the well known problems in understanding within nets the simple notion of syntactic substitution of conditions by (sub) nets behaviourally, - these problems seem to disappear when moving to the more abstract level of ETS. Formally, we show that the ETS-version of condition-substitution does satisfy nice and natural properties, e.g., projection and compositionality results w.r.t. a standard notion of transition system morphisms.

scholarly journals Transition Systems, Event Structures and Unfoldings

1991 ◽  
Vol 20 (353) ◽  
Author(s):  
Mogens Nielsen ◽  
Grzegorz Rozenberg ◽  
P. S. Thiagarajan
Keyword(s):  
Full Subcategory ◽  
Semantic Theory ◽  
Transition System ◽  
Transition Systems ◽  
Event Structures ◽  
Elementary Transition ◽  
Models Of Concurrency ◽  
The Right

<p>Elementary transition systems were introduced by the authors in DAIMI PB-310. They were proved to be, in a strong categorical sense, the transition system version of elementray net systems. The question arises whether the notion of a region and the axioms (mostly based on regions) imposed on ordinary transition systems to obtain elementray net systems. Stated differently, one colud ask whether elementray transition systems could also play a role in characterizing other models of concurrency.</p><p> </p><p>We show here that by smoothly stengthening the axioms of elementary transition systems one obtains a subclass called occurrence transitions systems which turn out to be categorically equivalent to the well-known model of concurrency called prime event structures.</p><p> </p><p>Next we show that occurrence transition systems are to elementry transition systems what occurrence nets are to elementary nets systems. We define an ''unfold'' operation on elementry transition systems which yields occurrence transistion systems. We then prove that this operation uniquely extends to a functor which is the right adjoint to the inclusion functor from (the full subcategory of) occurrence transition systems to (the category of) elementary transition systems. Thus the results of this paper also show that the semantic theory of elementray net systems has a nice counterpart in the more abstract world of transition systems.</p>

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.

scholarly journals Relating Apartness and Bisimulation

2021 ◽  
Vol Volume 17, Issue 3 ◽  
Author(s):  
Herman Geuvers ◽  
Bart Jacobs
Keyword(s):  
Transition System ◽  
Proof System ◽  
Transition Systems ◽  
Labelled Transition Systems ◽  
Induction Principle ◽  
Weak Bisimulation ◽  
Initial Algebra ◽  
Branching Bisimulation ◽  
Dual Notion ◽  
Labelled Transition System

A bisimulation for a coalgebra of a functor on the category of sets can be described via a coalgebra in the category of relations, of a lifted functor. A final coalgebra then gives rise to the coinduction principle, which states that two bisimilar elements are equal. For polynomial functors, this leads to well-known descriptions. In the present paper we look at the dual notion of "apartness". Intuitively, two elements are apart if there is a positive way to distinguish them. Phrased differently: two elements are apart if and only if they are not bisimilar. Since apartness is an inductive notion, described by a least fixed point, we can give a proof system, to derive that two elements are apart. This proof system has derivation rules and two elements are apart if and only if there is a finite derivation (using the rules) of this fact. We study apartness versus bisimulation in two separate ways. First, for weak forms of bisimulation on labelled transition systems, where silent (tau) steps are included, we define an apartness notion that corresponds to weak bisimulation and another apartness that corresponds to branching bisimulation. The rules for apartness can be used to show that two states of a labelled transition system are not branching bismilar. To support the apartness view on labelled transition systems, we cast a number of well-known properties of branching bisimulation in terms of branching apartness and prove them. Next, we also study the more general categorical situation and show that indeed, apartness is the dual of bisimilarity in a precise categorical sense: apartness is an initial algebra and gives rise to an induction principle. In this analogy, we include the powerset functor, which gives a semantics to non-deterministic choice in process-theory.

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