## Modelling of Complex Software Systems: a Reasoned Overview

Citations: | 5 - 2 self |

### BibTeX

@MISC{Krob_modellingof,

author = {D. Krob},

title = {Modelling of Complex Software Systems: a Reasoned Overview },

year = {}

}

### OpenURL

### Abstract

This paper is devoted to the presentation of the key concepts on which a mathematical theory of complex (industrial) systems can be based. We especially show how this formal framework can capture the realness of modern information technologies. We also present some new modelling problems that are naturally emerging in the specific context of complex software systems.

### Citations

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Citation Context ...gns made in this formalism). Fig. 7. A Matlab/Simulink TM integrated system model c○. Example 6. Discrete formalisms – The last model that we would like to discuss in this section is Statecharts (see =-=[23, 35]-=-). It is indeed probably the very first model – introduced in 1987 – that allowed hierarchical design, one of the key idea of this formalism. In Statecharts, it is indeed possible to deal with distrib... |

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Citation Context ...d (see [12]) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. [31]) or Z (cf. =-=[52]-=-), any modelling tool coming from the model checking approach (cf. [6, 49]) or even any classical programming language, to describe the step-by-step behavior of an abstract system by a “logical” forma... |

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Citation Context ... for designing continuous systems (see [36]). Observe also that specific frameworks exist for dealing with several important families of continuous systems such as dynamical systems (cf. respectively =-=[28]-=- and [18] for the physical and the control theory point of views), Hamiltonian systems (cf. [40]), etc. Example 3. Hybrid systems – An abstract system will said to be hybrid when one of its input or o... |

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Citation Context ...lling tools that are now taking into account both physical and software frameworks (cf. for instance [8, 53] for the description of SysML that extends the classical Unified Modelling Language (UML) – =-=[46]-=- – for general systems). The purpose of this short paper is to make a reasoned overview on what could be a general theory of systems. After some preliminaries, we therefore present in Section 3 a tent... |

830 |
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Citation Context ...es such as Signal (see [32]) or Lucid (see [12]) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. =-=[1, 57]-=-), TLA+ (cf. [31]) or Z (cf. [52]), any modelling tool coming from the model checking approach (cf. [6, 49]) or even any classical programming language, to describe the step-by-step behavior of an abs... |

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Citation Context ... the other one is continuous. It is interesting to know that 5stwo types of approaches exist for studying hybrid systems, depending respectively whether one stresses on the discrete (see for instance =-=[2, 24]-=-) or the continuous point of view (see for instance [58]) with respect to such systems. However hybrid systems will of course always be represented by hybrid formalisms that mix discrete and continuou... |

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Citation Context ...ing discrete abstract systems in our meaning. There is also a purely logical approach for representing discrete abstract systems. The core modelling language in this direction is probably Lustre (cf. =-=[22, 13]-=-). This programming language is indeed structurally devoted to express transformations of typed infinite sequences. The Lustre program that models the (simple) behavior of our lamp is for instance giv... |

527 | The theory of hybrid automata
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Citation Context ... the other one is continuous. It is interesting to know that 5stwo types of approaches exist for studying hybrid systems, depending respectively whether one stresses on the discrete (see for instance =-=[2, 24]-=-) or the continuous point of view (see for instance [58]) with respect to such systems. However hybrid systems will of course always be represented by hybrid formalisms that mix discrete and continuou... |

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Citation Context ...ng aspects of Statecharts’ approach and to overcome its core flaws. For the sake of completeness, note finally that there are also other formal discrete formalisms that allow hierarchical design (see =-=[9]-=- and again [35]). 3.3 System abstraction and simulation Abstraction and simulation are two classical notions that can also be re-adapted to systems (we take below all the flow notations of the previou... |

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Citation Context ...ee [32]) or Lucid (see [12]) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. =-=[31]-=-) or Z (cf. [52]), any modelling tool coming from the model checking approach (cf. [6, 49]) or even any classical programming language, to describe the step-by-step behavior of an abstract system by a... |

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Citation Context ...ere we put c = (j, l) and χ −1 (c) = (i, k) in all these last relations. for c ∈ C I and t ≥ τ c ∈ T i k , Proof. The proof follows by using a classical argument of complete partial order theory (cf. =-=[21]-=-). Note that our result can be also seen as an extension of a classical result of Kahn (see [27]). ⊓⊔ This proposition translates now immediately in the following definition which gives a formal and p... |

119 |
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Citation Context ...aling with several important families of continuous systems such as dynamical systems (cf. respectively [28] and [18] for the physical and the control theory point of views), Hamiltonian systems (cf. =-=[40]-=-), etc. Example 3. Hybrid systems – An abstract system will said to be hybrid when one of its input or output time scales is discrete when the other one is continuous. It is interesting to know that 5... |

110 |
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Citation Context ...aches which capture quite well the event reacting 3sdimension of a real system. These types of formalisms all basically rely on the use of rational transducers – or equivalently Mealy machines – (cf. =-=[3, 37]-=-) for expressing the transfer function of a discrete system. Figure 1 shows a simple example of this kind of formalism for modelling the effect of the switch button of a lamp on its lighting performan... |

95 |
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Citation Context ...pressed or released). Fig. 4. Modelling the physical behavior of a lamp by an hybrid automaton. Other families of hybrid formalisms – in our meaning – can be typically found in signal processing (see =-=[43]-=-) for modelling demodulation or sampling (transformation of a continuous signal into a discrete one) and modulation (transformation of discrete signal into a continuous one). These last formalisms are... |

92 |
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Citation Context ...tween the approaches used for managing the engineering phases 2 of physical and of software systems. This convergence can in particular be seen at a methodological level since system engineering (see =-=[47, 55]-=-) and software engineering (see [48, 51]) are more or more expressing their methods in the same way, but also at the level of the architectural principles used in physical and software contexts (see [... |

84 |
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Citation Context ...ee how to get more realistic models with respect to the lamp real physical behavior (see Examples 2 and 3). Fig. 1. Modelling the transfer function of a lamp by a rational transducer. Petri nets (cf. =-=[42, 45]-=-), (min−max, +) systems (cf. [4]), Kahn networks (cf. [27]), etc. are other examples – among numerous others – of basic automaton-oriented formalisms that can be used (with slight modifications) for d... |

62 | Synchronous Kahn networks
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Citation Context ...ing discrete abstract systems in our meaning. There is also a purely logical approach for representing discrete abstract systems. The core modelling language in this direction is probably Lustre (cf. =-=[22, 13]-=-). This programming language is indeed structurally devoted to express transformations of typed infinite sequences. The Lustre program that models the (simple) behavior of our lamp is for instance giv... |

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Citation Context ...ave an holistic approach that integrates in the same common framework the software, the hardware, the physical and the control theory points of views and constraints involved within such systems (see =-=[25]-=-). One therefore naturally divides the design in two separated, but completely interconnected, main parts: the functional design that corresponds here to the global environment and solution modelling ... |

55 |
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Citation Context ...gns made in this formalism). Fig. 7. A Matlab/Simulink TM integrated system model c○. Example 6. Discrete formalisms – The last model that we would like to discuss in this section is Statecharts (see =-=[23, 35]-=-). It is indeed probably the very first model – introduced in 1987 – that allowed hierarchical design, one of the key idea of this formalism. In Statecharts, it is indeed possible to deal with distrib... |

44 |
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Citation Context ...nteractions (or equivalently interfaces) existing between the corresponding human and software systems. Fig. 10. An information system architecture (Sysoft c○) and a business process model (BPMN c○ – =-=[56]-=-). A business profess refers typically to an enterprise process such as billing, maintening, sourcing, producing, etc. Business process modelling (BPM) is therefore naturally one of the core methodolo... |

42 |
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Citation Context ...gning continuous systems (see [36]). Observe also that specific frameworks exist for dealing with several important families of continuous systems such as dynamical systems (cf. respectively [28] and =-=[18]-=- for the physical and the control theory point of views), Hamiltonian systems (cf. [40]), etc. Example 3. Hybrid systems – An abstract system will said to be hybrid when one of its input or output tim... |

34 |
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Citation Context ...Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. [31]) or Z (cf. [52]), any modelling tool coming from the model checking approach (cf. =-=[6, 49]-=-) or even any classical programming language, to describe the step-by-step behavior of an abstract system by a “logical” formalism. Example 2. Continuous systems – An abstract system will said to be c... |

28 |
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Citation Context ... probably result in the development of new methods for complex software quantitative analysis, an important subject which is still under-developed in the classical context of information systems (see =-=[19, 44]-=-) and basically non existing for systems of systems. One should finally not forget all the specific problems that are of course continuously emerging in the jungle of complex software systems. As a ma... |

27 |
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Citation Context ...es such as Signal (see [32]) or Lucid (see [12]) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. =-=[1, 57]-=-), TLA+ (cf. [31]) or Z (cf. [52]), any modelling tool coming from the model checking approach (cf. [6, 49]) or even any classical programming language, to describe the step-by-step behavior of an abs... |

26 |
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Citation Context ...essivity: the precise nature of the interactions between the two automata separated by the dashed line (which models concurrency) in Figure 8 is typically not totally clear. The Esterel language (see =-=[7]-=- or [5] where one can find a good overview of all so-called synchronous languages) was typically designed in order both to preserve the most interesting aspects of Statecharts’ approach and to overcom... |

17 |
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Citation Context ...y safe approach, as one may imagine, for obvious synchronization reasons . . . 11sExample 8. Interfaces – The interface theory which was recently developed by de Alfaro and Henziger (see for instance =-=[17]-=-) can easily be transferred into the system framework as presented here (with of course again a number of slight reinterpretations). System interfaces provide then new generic interesting examples of ... |

16 |
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Citation Context ...Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. [31]) or Z (cf. [52]), any modelling tool coming from the model checking approach (cf. =-=[6, 49]-=-) or even any classical programming language, to describe the step-by-step behavior of an abstract system by a “logical” formalism. Example 2. Continuous systems – An abstract system will said to be c... |

16 |
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Citation Context ... i.e. when the button switch is pressed (resp. released), which models correctly the expected behavior of the lamp (initially switched off) we considered. Other reactive languages such as Signal (see =-=[32]-=-) or Lucid (see [12]) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. [31]) o... |

15 |
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Citation Context ...efinition of a “good” global more restricted family of abstract systems that tries to capture the full realness of systems, using a Turing machine type formalism mixed with non standard analysis (cf. =-=[16]-=-) for taking into account the continuous and discrete dimensions of systems in the same framework. 6s3.2 Abstract integration Up to now, we only focused on “simple” models for dealing with systems. Qu... |

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Citation Context ...iples used in physical and software contexts (see [33]) and of the quasi-formal specifying and modelling tools that are now taking into account both physical and software frameworks (cf. for instance =-=[8, 53]-=- for the description of SysML that extends the classical Unified Modelling Language (UML) – [46] – for general systems). The purpose of this short paper is to make a reasoned overview on what could be... |

10 | Formal specification of non-functional properties of componentbased software systems: A semantic framework and some applications thereof,” Software and Systems Modelling (SoSyM
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Citation Context ...r framework. A non functional property N of a system can indeed typically always be measured either by some suited numerical indicator fN(t) or by an adapted boolean predicate PN(t) (see for instance =-=[60]-=-), depending on internal parameters of the considered system, that can be measured at each moment t of the input time. Such non functional properties can then be expressed in our framework by extendin... |

9 |
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Citation Context ...stributed algorithmic point of view. Example 13. Interoperability of systems of systems – When interoperability is a well known problem which is quite well mastered for usual information systems (see =-=[20, 34]-=-), it is probably still an open subject at the level of systems of systems. The key difficulty at this level comes 15sfrom the fact that one must interface in a coherent way a number of information sy... |

6 |
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Citation Context ...ith respect to the lamp real physical behavior (see Examples 2 and 3). Fig. 1. Modelling the transfer function of a lamp by a rational transducer. Petri nets (cf. [42, 45]), (min−max, +) systems (cf. =-=[4]-=-), Kahn networks (cf. [27]), etc. are other examples – among numerous others – of basic automaton-oriented formalisms that can be used (with slight modifications) for describing discrete abstract syst... |

5 |
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Citation Context ...aches which capture quite well the event reacting 3sdimension of a real system. These types of formalisms all basically rely on the use of rational transducers – or equivalently Mealy machines – (cf. =-=[3, 37]-=-) for expressing the transfer function of a discrete system. Figure 1 shows a simple example of this kind of formalism for modelling the effect of the switch button of a lamp on its lighting performan... |

5 |
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Citation Context ...ations, leading to a total cost of around 500 millions euros. At a deeper level, complex industrial systems are characterized by the fact that they are resulting of a complex integration process (cf. =-=[38, 39]-=- for more details). This means that such systems are obtained by integrating in a coherent way – that is to say assembling through well defined interfaces – altogether a tremendously huge number of he... |

5 |
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Citation Context ...tware systems (see Section 4). 2 I.e. design, architecture, integration and qualification processes. 2s2 Preliminaries As in the few previous attempts to discuss globally of systems (see for instance =-=[14, 50, 59]-=-), these objects will be defined here as mechanisms that are able to receive, transform and emit physical and/or informational quantities among time. This explains why we will first introduce two key ... |

4 |
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Citation Context ...y: the precise nature of the interactions between the two automata separated by the dashed line (which models concurrency) in Figure 8 is typically not totally clear. The Esterel language (see [7] or =-=[5]-=- where one can find a good overview of all so-called synchronous languages) was typically designed in order both to preserve the most interesting aspects of Statecharts’ approach and to overcome its c... |

4 | Towards a Functional Formalism for Modelling Complex Industrial Systems
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Citation Context ...at can be found in practice form only a “small” subfamily of the abstract systems covered by Definition 1 (which was only given here in such a generality for the sake of simplicity). One may found in =-=[29, 30]-=- a formal definition of a “good” global more restricted family of abstract systems that tries to capture the full realness of systems, using a Turing machine type formalism mixed with non standard ana... |

3 |
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Citation Context ...tware systems (see Section 4). 2 I.e. design, architecture, integration and qualification processes. 2s2 Preliminaries As in the few previous attempts to discuss globally of systems (see for instance =-=[14, 50, 59]-=-), these objects will be defined here as mechanisms that are able to receive, transform and emit physical and/or informational quantities among time. This explains why we will first introduce two key ... |

2 |
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Citation Context ...fficulty of integrating coherently the heterogeneous formal and informal models – going from partial differential equations and logical specifications to business process modelling (BPM) methods (cf. =-=[11]-=-) – that one must handle in order to deal globally with such systems. There is in particular still no real formal general models that can be used for dealing with complex industrial systems from a glo... |

2 |
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Citation Context ...tware systems (see Section 4). 2 I.e. design, architecture, integration and qualification processes. 2s2 Preliminaries As in the few previous attempts to discuss globally of systems (see for instance =-=[14, 50, 59]-=-), these objects will be defined here as mechanisms that are able to receive, transform and emit physical and/or informational quantities among time. This explains why we will first introduce two key ... |

2 |
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Citation Context ...ations, leading to a total cost of around 500 millions euros. At a deeper level, complex industrial systems are characterized by the fact that they are resulting of a complex integration process (cf. =-=[38, 39]-=- for more details). This means that such systems are obtained by integrating in a coherent way – that is to say assembling through well defined interfaces – altogether a tremendously huge number of he... |

2 |
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Citation Context ...tween the approaches used for managing the engineering phases 2 of physical and of software systems. This convergence can in particular be seen at a methodological level since system engineering (see =-=[47, 55]-=-) and software engineering (see [48, 51]) are more or more expressing their methods in the same way, but also at the level of the architectural principles used in physical and software contexts (see [... |

1 |
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Citation Context ...n switch is pressed (resp. released), which models correctly the expected behavior of the lamp (initially switched off) we considered. Other reactive languages such as Signal (see [32]) or Lucid (see =-=[12]-=-) are using too the same global flow manipulating approach. Note that one can of course also take any usual formal specification language such as B (cf. [1, 57]), TLA+ (cf. [31]) or Z (cf. [52]), any ... |

1 |
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Citation Context ...eal physical behavior (see Examples 2 and 3). Fig. 1. Modelling the transfer function of a lamp by a rational transducer. Petri nets (cf. [42, 45]), (min−max, +) systems (cf. [4]), Kahn networks (cf. =-=[27]-=-), etc. are other examples – among numerous others – of basic automaton-oriented formalisms that can be used (with slight modifications) for describing discrete abstract systems in our meaning. There ... |

1 |
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Citation Context ...ion), EAI (internal software integration), ETL (batch data consolidation) or EII (on the request data consolidation) softwares. We refer to [26] for an overview of these software technology (see also =-=[54, 34]-=-). – information systems: an information system can be defined as a coherent integration of several integrated softwares – in the above meaning – that supports all the possible business missions of an... |

1 |
Processus métiers et systèmes d’information
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(Show Context)
Citation Context ...ore be seen as the integrated system that consists both of a human organization and of all the computer systems that are supporting the specific business processes of the considered organization (see =-=[11, 41]-=- or Example 11 for more details). – systems of systems: this refers to an even higher level of integration, i.e. to the situation where a number of independently designed information systems have to c... |

1 |
Deh C., Mesdon B., Trèves B., Coûts et durée des projets informatiques – Pratique des modèles d’estimation, Hermès Lavoisier
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(Show Context)
Citation Context ... probably result in the development of new methods for complex software quantitative analysis, an important subject which is still under-developed in the classical context of information systems (see =-=[19, 44]-=-) and basically non existing for systems of systems. One should finally not forget all the specific problems that are of course continuously emerging in the jungle of complex software systems. As a ma... |

1 |
Analyse et conception de systèmes d’information, Les éditions Reynald Goulet
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Citation Context ...he engineering phases 2 of physical and of software systems. This convergence can in particular be seen at a methodological level since system engineering (see [47, 55]) and software engineering (see =-=[48, 51]-=-) are more or more expressing their methods in the same way, but also at the level of the architectural principles used in physical and software contexts (see [33]) and of the quasi-formal specifying ... |