Radu Grosu, Cornel Klein, Bernhard Rumpe, and Manfred Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....formalisms. On the other hand the reappearance of several different concepts within Spectrum implies also some problems on the semantical level. This applies especially to the known roots of Spectrum, algebraic data types combined with logic, domain theory, and type theory (see [BFG 93, GR93] Starting from this setting we motivate a general framework to express the formal relationship between different logical systems. The term logical system in this context denotes the syntactical and semantical concepts underlying most of the specification and programming languages. ....

....implications and possible compatibilities, is under development at the TU Berlin. A first proposal was presented at the COMPASS workshop 93 in Dresden [Wol95] This framework is based on the concept of institutions developed by Burstall and Goguen [GB92] and used by Grosu and Regensburger [GR93] for the description of the Spectrum semantics. The embedding of ACT ONE and Opal into Spectrum will be sketched in sec. 4 by means of that framework. In preparation for sec. 4 we give in sec. 3 a compact and informal presentation of the institutions of ACT ONE, Opal, and Spectrum. In the ....

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R. Grosu and F. Regensburger. The Logical Framework of Spectrum. Technical report, Technische Universitat Munchen, March 1994.

....spaces have to be continuous. Therefore functions which are non continuous or even non monotonic, as, for instance, internal boolean definedness functions, can be represented only by morphisms. In such a way currying becomes partial in cpo approaches allowing also non continuous functions (see [GR94]) Recursive function definitions The main justification for cpo approaches is, that they provide semantics for recursive function definitions. The crucial point is, that the recursive definition of a function f from A to B gives rise to a continuous functional F : A ) B) Gamma (A ) B) such ....

Radu Grosu and Franz Regensburger. The Logical Framework of spectrum. Technical Report TUM-I9402, Institut fur Informatik, Technische Universitat Munchen, 1994.

....polymorphism. It also provides a solution to the other kinds of polymorphism. But some problems are still open, e.g. the relation between parametric polymorphism and parameterized algebraic specifications. The specification language Spectrum uses shallow predicative polymorphism with type classes [437, 436]. Type classes allow to abstract from concrete sorts by using sort variables and to restrict the range of the sort variables to a given set of types. Technically, each type class is a sort and each type is an element of an order sorted algebra of type classes. For this kind of polymorphism, type ....

....predicative polymorphism with type classes, ffl parameterization and modularization. An informal introduction explaining the objectives and concepts of Spectrum by using simple, wellknown examples is given in [155, 156] The language definition, the semantics and the calculus are given in [434] [436] and [804] respectively. Spectrum incorporates the entire notation for typed terms. Therefore Spectrum supports partial and non strict functions as well as higher order functions. The models of Spectrum specifications are certain continous algebras [437, 436] Spectrum uses three valued logic ....

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R. Grosu and F. Regensburger. The Logical Framework of Spectrum. TUM-I 9402, Institut fur Informatik, Technische-Universitat Munchen, 1994.

.... in [BHH ] In the SysLab project, we use a mathematical system model ( RKB95] GRK96] which is based on stream processing functions [BDD 93] as a foundation for formalizing and integrating the various description techniques used in SysLab for specifying different system views ( Het96] GKRB96] GR96] The doctoral thesis corresponding to this paper will cover the definition of an adequate description technique for business process modeling, which is both intuitively understandable and semantically well defined. The definition of semantics and the relation to other description ....

....system behavior. As the description technique used for complete behavior modeling should especially accomodate the needs of the system developer with regard to expressiveness for generic complete behavior description, formality and tool support, in SysLab we turn to state transition diagrams [GKRB96] for specifying the complete behavior of system components. As both description techniques for system behavior are semantically integrated with respect to the mathematical system model, the information specified in the business process model is a start up for the state transition diagrams. The ....

R. Grosu, C. Klein, B. Rumpe and M. Broy. State Transition Diagrams. Technical Report TUM-I9630, Technische Universitat Munchen, Munchen, June 1996.

....postconditions defining the involved data changes, if only the effects on the state space and the triggering input and final output are relevant. If the full (interaction) behaviour of a service is relevant, it is described by an enhanced form of nondeterminstic input output automata defined in [GKRB96] In the example such an automaton is given for the read service. role pipe = f attributes Data : sequence of data partner reader, writer : any service write = f trigger input d : data from writer post Data = Data ffi d g service write close = f trigger from writer post Data = Data ffi ....

....choosing automata instead of process calculi like CSP [Hoa85] Also, automata can make the lifecycle of role data explicit. The major advantage of automata is their widespread use and ease of understanding. The latter is especially important for the architectural description which needs 1 In [GKRB96] this is extended to predicates characterizing data states to be communicated between software designers and users. pipe p1 split splitactor pipe p2 pipe p3 upper upperactor lower loweractor pipe p4 pipe p5 merge mergeactor pipe p6 Figure 2: Configuration Structure of CAPITALIZE A system is ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State transition diagrams. TUM-I 963O, Technische Universitat Munchen, 1996.

....system modules for execution in later stages of the system development process, we leave the cross functional, exemplaric view of business process modeling and turn to modeling the complete behavior of single system components or objects. At this stage, we employ automata or state machines ( GKRB96] for modeling component behavior. The methodic and semantic integration of these approaches is subject of ongoing research. Acknowledgements I thank Wolfgang Schwerin, Manfred Broy and Bernhard Rumpe for many fruitful discussions. ....

R. Grosu, C. Klein, B. Rumpe and M. Broy. State Transition Diagrams. Technical Report TUM-I9630, Technische Universitat Munchen, Institut fur Informatik, Munchen, June 1996.

..... 11 3.4 System Interface Model . 13 4 Summary 19 5 Conclusion 20 1 Introduction Within the SysLab project a set of description techniques (both graphical and textual) has been developed to represent different views of a software system [Thu97, Pae97, Het96, GKRB96]. Until now, the main effort has been to define a formal semantics for these descriptions and to integrate them into a mathematical system model [KRB96] In this paper we present an example of a software development in its early phases using some of the description techniques available 1 . We ....

....business oriented point of view, whereas the EERDs present a static data oriented view of the system. Now, during the late analysis phase, the SIM allows the developer to describe the whole system within a more formal, dynamic view based on its behaviour. It uses State Transition Diagrams (STD) [GKRB96] for both modeling dynamic system behaviour and formal specification of dynamic data constraints. The SIM specifies the system interface through externally triggered services, which represent a group of activities within a role of a BPM [Pae97] Therefore the concept of a role forms the connection ....

Radu Grosu, Cornel Klein, Bernhard Rumpe, and Manfred Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.

....Hus93] Tools for the formal development of software using Spectrum are still under development. Besides a language analyser for Spectrum, prototypical machine support for the verification task has been implemented at the Technical University of Munich. There is an instance of the Spectrum logic [Reg94] in the generic theorem prover Isabelle [Nip89] and a backend for the Spectrum parser [Pus94] that translates Spectrum specifications into Isabelle theories. For Opal, a comprehensive compilation system which produces highly efficient and portable code has been developed at the Technical ....

F. Regensburger. Der spectrum Kalkul in Isabelle. Interner Bericht, Technische Universitat Munchen, to appear, 1994.

.... in the project Prospectra [KBH91] and a more type theory oriented language like Lcf [WGM79, Pau87] An informal presentation with many examples illustrating its properties is given in [BFG 93a, BFG 93b] A description of the formal semantics of its kernel language can be found in [GR93] We now briefly summarize Spectrum s principal characteristics. Influences from algebra in SPECTRUM. In Spectrum specifications the influence of algebraic techniques is evident. Every specification consists of a signature and an axioms part. However, in contrast to most algebraic specification ....

R. Grosu and F. Regensburger. The logical framework of spectrum. Interner Bericht, Technische Universitat Munchen, 1993.

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Radu Grosu, Cornel Klein, Bernhard Rumpe, and Manfred Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.

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R. Grosu: A Formal Foundation for Concurrent Object Oriented Programming, Dissertation, Technische Universitat Munchen, 1995

....We do not elaborate on the underlying type system here, but assume an appropriate one to be given. In addition, to add a precise characterization of behavioral concepts, a mapping of the above given definitions into a system model as given in [KRB96] using state machines as behavioral entities [PR97, GKRB96] could be defined. 2.3 A Model for Component Based Systems Our model for a component based system is introduced on top of the model for objectoriented systems. Definition 4 Component A Component (name; os; pr; If; Int) is given by ffl a unique name for the component, ffl an underlying object ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State Transition Diagarams. Technical Report TUM-I9630, Technische Universitat Munchen, 1996.

....of data states and to have control states represented. As the input of a component is timed, we have to accept input messages at every time. To get a further degree of description freedom we decide to add an input buffer for not yet processed input messages and thus get a state space similar to [GKRB96] The state space of every basic component c 2 ID b can be seen as: State c = In c D ) Theta Data c Theta (Out c D ) and the initial state space as: State 0 c ffflg Theta Data c Theta ffflg where Data c is the data space of a basic component. 6.7 Sorts in the System Model The ....

....on every line in each time interval, is however sufficient. To get a reactive automaton ffi nor j , we extend the automaton by adding auxiliary transitions for the other input possibilities. These transitions may for instance lead to a state in which arbitrary (chaotic) behavior is possible (see [GKRB96] While chaotic behavior is adequate in software systems, for the modeling of hardware systems a less liberal behavior in these cases might be adequate. The reason is that sending a gate more than one message within one interval of time usually will not lead to arbitrary behavior in the future, ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State Transition Diagrams. Technical Report TUM I9630, Technische Universitat Munchen, 1996. 40

....for the exposition here, we do not elaborate concurrency issues and instead focus on features as refinement. Many other models and notations for specifying behavior have been developed. Examples for graphical notations are SDL process graphs [5] statecharts [15] state transition diagrams ([14], 23] Other, formally based approaches are I O automata [20] or TLA [19] We claim that our model combines the advantages of a graphical notation with elaborated and formal refinement rules. The paper is structured as follows. In the following section, we briefly introduce our system model. ....

....for software specification and development, graphical and textual notations are needed, which provide a convenient user interface to formal models for software systems. Therefore, in this section we introduce a graphical description technique state transition diagrams along the lines of [14, 23, 22] for the specification of components in our semantic model. State transition diagrams are based on the concept of a state machine (STM) which we introduce first. A state machine describes the behavior of a component using states of the component and transitions between states. There are two ....

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Radu Grosu, Cornel Klein, Bernhard Rumpe, and Manfred Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.

....a transition is attributed with a set of messages (sometimes restricted to one message) to be processed during the transition and a set of messages to be produced. There are timed and untimed variants, and there are variants incorporating pre and postconditions on transitions [RK96,PR94,GKR96,GKRB96,GR95,Rum96,PR97a] In the object oriented flavor, State Transition Diagrams describe the lifecycle of objects. In STDs, descriptions of state and behavior are combined. STDs can be used at different levels of abstraction that allow both the specification of an object interface as well as the ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State Transition Diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.

....phase they can help to improve the dialog between customers and application experts. HySCs complement existing formalisms like hybrid automata by focusing on the interaction between the system s components. A detailed presentation of HySCs together with their formal semantics is given in [6]. 1 Introduction Requirements engineering for embedded systems usually necessitates to take intrinsic properties of the system s environment into account. In many cases, e.g. in Currently on leave at School of Engineering and Applied Science, Department of Computer and Information Science, 200 ....

.... by the beneficial role interaction based description techniques, like [7, 8, 3, 2] play in the requirements specification of telecommunication and, more generally, object oriented systems, we developed hybrid sequence charts (HySCs) in the attempt to carry over these advantages to hybrid systems [6]. HySCs may be seen as relatives of trajectories and timing diagrams. Trajectories probably are the most basic approach to visualizing a system s evolution. They consist of drawing plots of the evolution of the system s variables over the time axis (Fig. 1, top left) A more abstract description ....

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R. Grosu, I. Kruger, and T. Stauner. Hybrid sequence charts. Technical Report TUM-I9914, Technische Universitat Munchen, 1999.

....unclear and is left to the interpretation of the system designer. The focus of our paper is to provide clear concepts and techniques for the dynamic modeling of objects in concurrent environments. The central description technique we rely on is a powerful variant of state transition diagrams [4, 3]. In these diagrams, transitions are associated with triples consisting of a precondition (the guard) a set of input output events and a postcondition describing the change of state. The notion of methods we consider is more general than the notion of procedures in a programming language. In our ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State Transition Diagrams. Technical Report TUM-I9606, Technische Universitat Munchen, June 1996.

....Finally we draw some conclusions in section 7. Note that space limitations caused us to leave out the treatment of generation constraints and of constructs related to specifying in the large (e.g. signature morphisms, reducts and logical relations between algebras) A full treatment is given in [10]. 2 Some Motivating Examples Before discussing the more involved technicalities of Spectrum we present some motivating examples. They will help to better appreciate the design decisions made in Spectrum and to get more intuition about its syntax and semantics. We start by giving a polymorphic ....

....the concrete syntax a specification S = Sigma; E) is a pair where Sigma = Omega ; F; O) is a polymorphic signature and E is a set of Sigma formulae. The definitions for Sigma and for its components Omega ; F and O are sketched in the text below. For a detailed presentation we refer to [10]. Definition1 Sort Signature. A sort signature Omega = K; SC) is an order sorted signature 2 , where (K; is a partial order on kinds, SC = fSCw;k g w2(Knfmapg) k2K is an indexed set of sort constructors with monotonic functionalities i.e. sc 2 SCw;k SCw 0 ;k 0 ) w w 0 ....

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R. Grosu and F. Regensburger. The Logical Framework of spectrum. Technical Report TUM-I9402, Institut fur Informatik, Technische-Universitat Munchen, 1994.

....Finite Behavior. The HHSCs i2o and o2i are examples for HySCs that do not specify infinite behavior. Instead of feedback arrows, an arrow leading to a black triangle is drawn in them to mark their end. As they are fairly straightforward, we omit them in this paper and refer the reader to [7]. 3.2.2 Basic HySCs All the basic HySCs referenced directly or indirectly by HHSC outBend describe the behavior of the EHC in the interval between two expirations of the Controller s timer. In the following we will analyze HySC i2d in detail. This HySC describes the scenario in which the chassis ....

.... j 9v 2 R : v) 2 [ M 1 ] u ( t) 2 [ M 2 ] v g Note that whereas the HySC M 1 ; M 2 may describe an infinite computation (t 2 R 1 ) any of its prefixes exhibiting the behavior required by M 1 has to be finite (v 2 R ) 4. 3 HHSCs Due to space limitations the reader is referred to [7] for the detailed semantics of nondeterministic choice, feedback and (nested) preemption. Basically, the semantics of feedback is obtained by a fixed point construction. The definition for preemption is rather technical and in large parts similar to the semantics definition for single event HySCs ....

R. Grosu, I. Kruger, and T. Stauner. Hybrid sequence charts. Technical Report TUM-I9914, Technische Universitat Munchen, 1999.

....and contains the SDL and the ROOM models as a particular case, in which all timing constraints equal true. This allows for a modular specification formalism along the lines of [BDD 93, BS97, GS96] and for a stepwise development process, where timing constraints are omitted in the first step [GKRB96] and introduced gradually in the next steps. The above would not hold, however, if we would change our model such that transitions are taken as soon as they become enabled. Moreover, in this case one would also have to introduce prophecies in order to express an arbitrary delay within a given ....

Radu Grosu, Cornel Klein, Bernhard Rumpe, and Manfred Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996.

....and understandability of the semantics definition considerably. For the semantics definition we employ our experience gained during the SysLab project. In SysLab the formally founded analysis and design method SLM has been developed covering description techniques similar to those of UML [18, 13, 12, 15, 22, 30]. Thus on the one hand we outline the basic ideas and the overall structure of the formal foundation of UML. This foundation revealed several language features which are not yet fully clear. We discuss some of these aspects in the respective sections. On the other hand we compare the description ....

....for instance, using sequence diagrams, to complete specifications using state diagrams. Formalization We formalize sequence diagrams by adopting a state box view. For each vertical line in a sequence diagram that corresponds to an object an abstract state automaton is defined along the lines of [12]. State automata consist of a set of states, an initial state, and a set of transitions. In our case, a transition is either labeled by an input event or by an output event. State automata can easily be translated into state transition systems of the system model [12] but this is not exploited ....

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R. Grosu, C. Klein, B. Rumpe, and M. Broy. State transition diagrams. TUM-I 9630, Technische Universitat Munchen, 1996. http://www4.informatik.tumuenchen. de/reports/TUM-I9630.html.

....to increase the readability and understandability of the semantics definition considerably. For the semantics definition we employ our experience gained during the SysLab project. In SysLab a formally founded design method has been developed covering description techniques similar to those of UML [18, 13, 12, 15, 21, 29]. The intention of this paper is to outline the basic ideas and the overall structure of the formal foundation of UML. Through the semantic definition of UML concepts, we detected a number of language features which are not yet fully clear. We discuss some of these aspects in the respective ....

....for instance, using sequence diagrams, to complete specifications using state diagrams. Formalization We formalize sequence diagrams by adopting a state box view. For each vertical line in a sequence diagram that corresponds to an object an abstract state automaton is defined along the lines of [12]. State automata consist of a set of states, an initial state, and a set of transitions. In our case, a transition is either labeled by an input event or by an output event. State automata can easily be translated into state transition systems of the system model [12] but this is not exploited ....

[Article contains additional citation context not shown here]

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State transition diagrams. TUMI 9630, Technische Universitat Munchen, 1996. http://www4.informatik.tumuenchen. de/reports/TUM-I9630.html.

....diagrams in which state transitions can be associated with outgoing events and state transitions can be guarded by preconditions and followed by postconditions. The kind of state transition diagrams we propose are well founded and provided with a formal semantics in a concurrent setting of objects [6, 4]. The notion of methods we conceive is more general than to be an equivalent to procedures in a programming language. In our intuition, methods in the analysis phase model high level activities of objects. Examples for such methods are the transfer of money in a bank or the reservation of a hotel ....

R. Grosu, C. Klein, B. Rumpe, and M. Broy. State Transition Diagrams. Technical Report TUM-I9606, Technische Universitat Munchen, June 1996.

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R. Grosu, C. Klein, B. Rumpe and M. Broy. State Transition Diagrams. Technical Report TUM-I9630, Technische Universitat Munchen, Institut fur Informatik, Munchen, June 1996.

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