scholarly journals Foundations of Modular SOS

1999 ◽  
Vol 6 (54) ◽  
Author(s):  
Peter D. Mosses
Keyword(s):  
Programming Languages ◽  
Transition System ◽  
Transition Systems ◽  
Labelled Transition System

A novel form of labelled transition system is proposed, where<br />the labels are the arrows of a category, and adjacent labels in computations<br /> are required to be composable. Such transition systems provide the<br />foundations for modular SOS descriptions of programming languages.<br />Three fundamental ways of transforming label categories, analogous to<br />monad transformers, are provided, and it is shown that their applications<br />preserve computations in modular SOS. The approach is illustrated with<br />fragments taken from a modular SOS for ML concurrency primitives.

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 Labelled transition system approach to distributed computing systems

2016 ◽  
Vol 8 (3) ◽  
pp. 19-32
Author(s):  
Dang Van Hung
Keyword(s):  
Distributed Computing ◽  
System Approach ◽  
Transition System ◽  
Distributed Computing Systems ◽  
Computing Systems ◽  
Transition Systems ◽  
Local Process ◽  
Global Properties ◽  
Labelled Transition System

The present paper introduces the  notion of  distributed transition systems for modeling, designing and  understanding distributed computing systems. The concurrency can be expressed explicitly in the model. Some of  the  global properties of the  systems are discussed and determined. It is  shown in the paper that  by keeping knowledge of other processes in each process of a system, some of its global properties can be synthesized from only few local process states.

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.

A domain equation for refinement of partial systems

2004 ◽  
Vol 14 (4) ◽  
pp. 469-505 ◽  
Author(s):  
MICHAEL R. A. HUTH ◽  
RADHA JAGADEESAN ◽  
DAVID A. SCHMIDT
Keyword(s):  
Transition System ◽  
Reactive System ◽  
Static Structure ◽  
Transition Systems ◽  
Temporal Properties ◽  
Modal Transition Systems ◽  
Partial Systems ◽  
Partial Bisimulation ◽  
Labelled Transition System ◽  
Mixed Transition

A reactive system can be specified by a labelled transition system, which indicates static structure, along with temporal-logic formulas, which assert dynamic behaviour. But refining the former while preserving the latter can be difficult, because:(i) Labelled transition systems are ‘total’ – characterised up to bisimulation – meaning that no new transition structure can appear in a refinement.(ii) Alternatively, a refinement criterion not based on bisimulation might generate a refined transition system that violates the temporal properties.In response, Larsen and Thomson proposed modal transition systems, which are ‘partial’, and defined a refinement criterion that preserved formulas in Hennessy–Milner logic. We show that modal transition systems are, up to a saturation condition, exactly the mixed transition systems of Dams that meet a mix condition, and we extend such systems to non-flat state sets. We then solve a domain equation over the mixed powerdomain whose solution is a bifinite domain that is universal for all saturated modal transition systems and is itself fully abstract when considered as a modal transition system. We demonstrate that many frameworks of partial systems can be translated into the domain: partial Kripke structures, partial bisimulation structures, Kripke modal transition systems, and pointer-shape-analysis graphs.

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 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.

scholarly journals Study on Formal Modeling and Safety Verification of Train-to-Train Communication

2018 ◽  
Vol 2018 ◽  
pp. 1-9
Author(s):  
Haonan Feng
Keyword(s):  
Transition System ◽  
Research Trend ◽  
Safety Properties ◽  
Safety Verification ◽  
Critical System ◽  
Real Time System ◽  
Vehicle Communication ◽  
Train Control ◽  
Safety Critical System ◽  
Labelled Transition System

VBTC (vehicle-to-vehicle communication based train control) has gradually become an important research trend in the field of rail transit. This has resulted in advantages of decreasing the number of pieces of wayside equipment and improving the efficiency of real-time system communication. Characteristics and mechanism of train-to-train communication, as key implementation technology of safety critical system, are given and discussed. A new method, based on the LTS (labelled transition system) model checking, is proposed for verifying the safety properties in the communication procedure. The LTS method is adapted to model system behaviours; analysis and safety verification are checked by means of LTSA (labelled transition system analyzer) software. The results show that it is an efficient method to verify safety properties, as well as to assist the complex system’s design and development.

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.

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