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 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>

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 Bisimulation from Open Maps

1994 ◽  
Vol 1 (7) ◽  
Author(s):  
André Joyal ◽  
Mogens Nielsen ◽  
Glynn Winskel
Keyword(s):  
Petri Nets ◽  
Parallel Computation ◽  
Transition Systems ◽  
New Model ◽  
Event Structures ◽  
Uniform Definition ◽  
Refinement Operators ◽  
Definition Of ◽  
Open Maps

An abstract definition of bisimulation is presented. It enables a uniform definition of bisimulation across a range of different models for parallel computation presented as categories. As examples, transition systems, synchronisation trees, transition systems with independence (an abstraction from Petri nets) and labelled event structures are considered. On transition systems the abstract definition readily specialises to Milner's strong bisimulation. On event structures it explains and leads to a revision of history-preserving bisimulation of Rabinovitch and Traktenbrot, Goltz and van Glabeek. A tie-up with open maps in a (pre)topos, as they appear in the work of Joyal and Moerdijk, brings to light a promising new model, presheaves on categories of pomsets, into which the usual category of labelled event structures embeds fully and faithfully. As an indication of its promise, this new presheaf model has ``refinement'' operators, though further work is required to justify their appropriateness and understand their relation to previous attempts. The general approach yields a logic, generalising Hennessy-Milner logic, which is characteristic for the generalised notion of bisimulation.

scholarly journals Architecture of Component-based Information Systems over the J2EE Platform

2018 ◽  
Vol 8 (1) ◽  
Author(s):  
Daniel Perovich ◽  
Leonardo Rodrıguez Rodrıguez ◽  
Andres Vignaga
Keyword(s):  
Information Systems ◽  
Methodological Approach ◽  
Logical Structure ◽  
The Other ◽  
Model Driven ◽  
J2ee Platform ◽  
Component Based Development ◽  
Abstract Level ◽  
Definition Of ◽  
Different Levels

Component-based development can be addressed from two different fronts, or more precisely, from two different levels. One of them regards the technology used for system implementation, and the other is a previous and more abstract level, where the focus is set to the logical structure of the solution and where technological issues are not considered. Model Driven Architecture promotes such separation by distinguishing platform independent models from platform specific models. In alignment with this approach, this article proposes a mapping from the tiered and platform independent architecture for information systems resulting from the application of a widely known methodological approach, to the available constructs in the J2EE platform. This mapping allows the definition of transformations between platform independent models, resulting from the referred methodology where it is possible to abstractly reason about the solution, and platform specific models which are aligned with technological constructs and are directly implemented.

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.

Hierarchical Design Method for Multi-Agent Systems

2015 ◽  
Vol 7 (2) ◽  
pp. 105-134
Author(s):  
Bouneb Messaouda ◽  
Saïdouni Djamel Eddine
Keyword(s):  
Design Methodology ◽  
Design Method ◽  
Transition System ◽  
Hierarchical Design ◽  
Multi Agent Systems ◽  
Agent Systems ◽  
Multi Agent ◽  
Labeled Transition System ◽  
System Assessment ◽  
Definition Of

This paper proposes a new hierarchical design method for the specification and the verification of multi agent systems (MAS). For this purpose, the authors propose the model of Refinable Recursive Petri Nets (RRPN) under a maximality semantics. In this model, a notion of undefined transitions is considered. The underlying semantics model is the Abstract Maximality-based Labeled Transition System (AMLTS). Hence, the model supports a definition of a hierarchical design methodology. The example of goods transportation is used for illustrating the approach. For the system assessment, the properties are expressed in CTL logic and verified using the verification environment FOCOVE (Formal Concurrency Verification Environment).

scholarly journals Approximate Analyzing of Labeled Transition Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-9
Author(s):  
Qiong Yu ◽  
Shihan Yang ◽  
Jinzhao Wu
Keyword(s):  
Control Systems ◽  
Linear Systems ◽  
Matrix Decomposition ◽  
Transition System ◽  
Formal Semantic ◽  
Semantic Model ◽  
Transition Systems ◽  
State Space Explosion ◽  
Normal Circumstance ◽  
Time Linear

As the most important formal semantic model, labeled transition systems are widely used, which can describe the general concurrent systems or control systems without disturbance. However, under normal circumstance, transition systems are complex and difficult to use due to large amount of calculation and the state space explosion problems. In order to overcome these problems, approximate equivalent labeled transition systems are proposed by means of incomplete low-up matrix decomposition factorization. This technique can reduce the complexity of computation and calculate under the allowing errors. As for continuous-time linear systems, we develop a modeling method of approximated transition system based on the approximate solution of matrix, which provides a facility for approximately formal semantic modeling for linear systems and to effectively analyze errors. An example of application in the context of linear systems without disturbances is studied.

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 Natural Quantum Operational Semantics with Predicates

2008 ◽  
Vol 18 (3) ◽  
pp. 341-359 ◽  
Author(s):  
Marek Sawerwain ◽  
Roman Gielerak
Keyword(s):  
Positive Operator ◽  
Operational Semantics ◽  
General Definition ◽  
Completely Positive Maps ◽  
Transition Systems ◽  
Positive Operator Valued Measures ◽  
Labelled Transition Systems ◽  
Positive Maps ◽  
Definition Of ◽  
Positive Operator Valued Measure

Natural Quantum Operational Semantics with PredicatesA general definition of a quantum predicate and quantum labelled transition systems for finite quantum computation systems is presented. The notion of a quantum predicate as a positive operator-valued measure is developed. The main results of this paper are a theorem about the existence of generalised predicates for quantum programs defined as completely positive maps and a theorem about the existence of a GSOS format for quantum labelled transition systems. The first theorem is a slight generalisation of D'Hondt and Panagaden's theorem about the quantum weakest precondition in terms of discrete support positive operator-valued measures.

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