scholarly journals Elementary transition systems

1990 ◽  
Vol 19 (310) ◽  
Author(s):  
Mogens Nielsen ◽  
Grzegorz Rozenberg ◽  
P. S. Thiagarajan
Keyword(s):  
Distributed Systems ◽  
Transition Systems ◽  
Common Framework ◽  
Elementary Transition ◽  
Models Of Concurrency ◽  
Operational Behaviour

<p>Transition systems are a simple and powerful formalism for explaining the operational behaviour of models of concurrency. They provide a common framework for investigating the interrelationships between different approaches to the study of distributed systems. Hence an important question to be answered is: which subclass of transition systems corresponds to a particular model of distributed systems? In this paper we provide an answer to this question for elementary net systems.</p>

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 Elementary transition systems

1992 ◽  
Vol 96 (1) ◽  
pp. 3-33 ◽  
Author(s):  
M. Nielsen ◽  
G. Rozenberg ◽  
P.S. Thiagarajan
Keyword(s):  
Transition Systems ◽  
Elementary Transition

scholarly journals Elementary transition systems and refinement

1992 ◽  
Vol 29 (6-7) ◽  
pp. 555-578 ◽  
Author(s):  
M. Nielsen ◽  
G. Rozenberg ◽  
P. S. Thiagarajan
Keyword(s):  
Transition Systems ◽  
Elementary Transition

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.

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.

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