F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [BK90], 401--415. (pp 16, 17)  Home/Search   Document Not in Database   Summary   Related Articles   Check

....tics pres ted below. The inferencerules define a mapping ofthis algebra ontoCTMCs (as we will sll9 (# i ) i j P j (j recX. recX. Th prefix(#) P can be considered as th probabilistic version of th timed prefix (t) P thx typically occurs in timed process algebras, like in TCCS [44] or in Timed CSP [50] H. Hermanns and J. P. Katoen The rule forrecurs [ is surs [ wejus recall that P Q X denotes term P in which all (free) occurrences of pro ces variable X in P are replaced by Q. The rule for choicerequires squ explanation.Consana i#I (# i ) i . At execution, thefas[4G ....

....either P or Q independently from (and concurrently to) each other. Due to the memory les property ofCTMCs the behaviour of parallelCTMCs can be interleaved. This is di#erent from adeterminis timesme9]4 where parallel proces4S typically are forced tos91 hronis on the advance of time,as in TCCS [44]. The operationalrules are: i,#) P # (#,i) Q #. Notice that we create new auxiliary labels of the form (i, and (#,i) in order to obtain a multi trans :9s relation. ToundersC] the meaning of the memoryles property in our contextcons1S[ the pro (#) and sd9 os that ....

F. Moller and C. Tofts. A temporal calculus for communicating systems. In CONCUR'90, LNCS 458:401--415. Springer, 1990.

....[27] However, in the literature we see more and more that SOS definitions are decorated with predicates and or negative premises. For example, predicates are used to express matters like (un)successful termination, convergence, divergence [10] enabledness [41] maximal delay, and side conditions [165]. Negative premises are used to describe, e.g. deadlock detection [137] sequencing [55] priorities [24, 65] probabilistic behaviour [139] urgency [58] and various real [136] and discrete time [23, 127, 223] settings. Since predicates and negative premises are so pervasive, and often lead to ....

F. Moller and C. Tofts, A temporal calculus of communicating systems, in Baeten and Klop [26], pp. 401--415.

....where the system ages [NS92] For actions whose duration is such that they cannot be abstracted as instantaneous, it suces to split them into a beginning and an ending action. This principle has lead to many extensions of well known process algebras, such as Timed CSP [RR88, DS94] Timed CCS [MT90, Wan91, Han91], Timed ACP [BB91, BB96, Gro90] and Timed LOTOS [MFV94, CdO94, BLT94b, BLT94a, LL97, LL98, QMdFL94] New timed process algebras have also been proposed, such as TPL [HR95] and ATP [NS94] Even though these languages propose interesting facilities to specify realtime behaviours, very few of them ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.C.M. Baeten and J.W. Klop, editors, CONCUR'90, Theories of Concurrency: Uni cation and Extension, volume 458 of LNCS, pages 401-415. Springer, Berlin, 1990.

.... is an extended and improved version of [LeL93, Le # L94] In particular, the language presented in [Le # L94] has been enhanced and slightly modified to cover full LOTOS (i.e. LOTOS with data types) Among the other proposals that have inspired us, let us mention Real Time CSP [ReR88] TCCS [MoT90] and the Calculus of Real Time Systems [Wan91] A detailed comparison with these proposals, and others, is provided in Section 8. In this paper we present ET LOTOS from a theoretical point of view. Its expressive power as a specification language is further demonstrated in another paper [Le # ....

....(P, #, P#) denoted P# P# in the sequel, may be read as : the process P may perform the action # and thereby be transformed into the process P#. We will sometimes write that the process is in the state P#. We keep this model for ET LOTOS. Following an idea first introduced by Moller and Tofts [MoT90] we simply extend it with a new kind of transitions : timed transitions. More precisely, we extend the set A of actions with D, the time domain. A transition labelled with a time value d, P# P#, means then : the process P may idle for d time units and thereby be transformed into the ....

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Moller, F., Tofts, C. : A temporal calculus of communicating systems. In : J. C. M. Baeten, J. W. Klop, eds., CONCUR '90, Theories of Concurrency : Unification and Extension, LNCS 458. Springer-Verlag, Berlin, 1990, 401--415.

.... modified to cover full LOTOS (i.e. LOTOS with data types) It is the basis of the timed extension of LOTOS currently developed in the ISO#IEC JTC1#SC33 standardization committee [ISO98] It has been inspired in one way or another by several other languages, such as Real Time CSP [ReR88] TCCS [MoT90] and the Calculus of Real Time Systems [Wan91] 2. Overview of the Paper In standard LOTOS, a system can only change state by performing actions, either internally or by interacting with its environment. Since the aim of ET LOTOS is to allow the description of the influence of time on the ....

....(P, #, P#) denoted P# P# in the sequel, may be read as : the process P may perform the action # and thereby be transformed into the process P#. We will sometimes write that the process is in the state P#. We keep this model for ET LOTOS. Following an idea first introduced by Moller and Tofts [MoT90] we simply extend it with a new kind of transitions : timed transitions. More precisely, we extend the set A of actions with D, the time domain. A transition labelled with a time value d, P# P#, means then : the process P may idle for d time units and thereby be transformed into the process ....

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Moller, F. and Tofts, C. : A temporal calculus of communicating systems. In : J. C. M. Baeten, J. W. Klop, eds., CONCUR '90, Theories of Concurrency : Unification and Extension, LNCS 458, Springer -- Verlag, Berlin, 1990, 401--415.

....this problem in this paper. In the untimed setting, bisimulation equivalences have been reasonably successful as notions of implementation between transition systems [BW90, Mil89] Consequently, bisimulation equivalences have also been proposed as implementation relations for the timed setting [BB91, Klu93, MT90, NS94, Yi90]. However, we do not believe that bisimulations will turn out to be very useful as implementation relations in the timed case. The problem is that they do not allow one to abstract in specifications from the often very complex timing behaviour of implementations (see Chapter 10 of [Klu93] for an ....

....that can block the passage of time, and a RATE operation that can change the speed of its argument. On the other hand, there are several operators that have been proposed in the literature that do not fit our format of action transducers, in particular, the CCS style choice operation present in [BB91, MT90, NS94, Yi90]. This operation cannot be expressed as a timed action transducer because the timed trace inclusion relation is not substitutive with respect to it. We briefly consider the design of an appropriate language of operators for describing timing based systems. Such a language should consist of a ....

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [BK90], pages 401--415.

....i.e. it is not suitable to take into account real time aspects. This is not the purpose of our formalism. We consider insertion of these properties as another level of abstraction. It is possible to introduce them in a refinement step following this specification step. Another idea is to use TCCS [10, 39] (T for Timed) instead of CCS. We remind that in CCS the synchronization is possible only between two agents. We have studied the modification of this kind of synchronization to another one. After much thoughts on the possible choices concerning the synchronization types: between two agents, ....

....execute themselves between two units of logical time to preserve the specification consistency. These hypotheses are non formal, then that could lead to inconsistencies. This drawback is due to the lack of real time constraints possibilities. A solution would be using a version of timed CCS [10, 39] in order to express the possible temporal aspects in a formal way. This is one of the main direction for future works. ClockAux(t: Instant, nbt: Nat, nbat: Nat) if (nbt = 1) then incClock.Clock(t, nbt, nbt) if not (nbt = 1) then incClock.ClockAux(t, nbt, nbat 1) The tester has ....

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F. Moller and C. Tofts. A Temporal Calculus of Communicating Systems. In J. C. M. Baeten and J. W. Klop, eds., Theories of Concurrency: Unification and Extension (CONCUR'90), volume 458 of Lecture Notes in Computer Science, pages 401--415, The Netherlands, 1990. Springer-Verlag.

....limiting the complexity of the method, this also reduces its expressiveness. As discussed in Section 3.4, an explicit notion of time is required to achieve a satisfactory speci cation of real time behaviour. TCCS is a process algebras with explicit time, and thus suitable for real time systems [MT90] It is based on CCS, but with two additional constructs. The term (t) P denotes a process that behaves as P after exactly t units of time, and :P behaves as P but is willing to wait any amount of time before actually proceeding. These constructs can be used to de ne useful real time concepts ....

Faron Moller and Chris Tofts. A temporal calculus of communicating systems. In J. C. M. Baeten and J. W. Klop, editors, CONCUR '90: Theories of Concurrency: Uni cation and Extension, volume 458 of Lecture Notes in Computer Science, pages 401-415, Amsterdam, The Netherlands, 27-30August 1990. Springer-Verlag.

....systems require considerable refinement of the process algebras, in both the algebraic notation as well as the underlying semantic models. Considerable effort in this latter area has resulted in a large collection of real time versions of untimed process al gebras, such as CCS (e.g. M83, MT90, W91b, HR95, H91, FZ95] CSP (e.g. RR88, S91, DS95, S96] and ACP (e.g. IBB91, NS94] Ever since the boom of the mobile communica tions industry in the 90 s, various mobile devices have been manufactured. As a result, mobile computing has gained more and more attention over the past decade. ....

F. Moller and C. Torts, "A Temporal Cal- culus of Communicating Systems", Proceedings of CONCUR'90, LNCS 458, p401-415, 1990.

....address this problem in this paper. In the untimed setting, bisimulation equivalences have been reasonably successful as notions of implementation between transition systems [6, 34] Consequently, bisimulation equivalences have also been proposed as implementation relations for the timed setting [4, 23, 35, 38, 47]. However, we do not believe that bisimulations will turn out to be very useful as implementation relations in the timed case. The problem is that they do not allow one to abstract in specifications from the often very complex timing behavior of implementations (see Chapter 10 of [23] for an ....

....that can block the passage of time, and a RATE operation that can change the speed of its argument. On the other hand, there are several operators that have been proposed in the literature that do not fit our format of action transducers, in particular, the CCS style choice operation present in [4, 35, 38, 47]. This operation cannot be expressed as a timed action transducer because the timed trace inclusion relation is not substitutive with respect to it. We briefly consider the design of an appropriate language of operators for describing timing based systems. Such a language should consist of a ....

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [5], pages 401--415.

.... I II) and as [43] 1 Introduction Most of the existing semantic models, languages and logics for describing and reasoning about timing based systems implicitly view an execution as an alternating sequence of instantaneous discrete actions and continuous phases during which time advances [2, 5, 7, 8, 9, 11, 14, 17, 20, 25, 26, 27, 48, 50, 52, 54, 61, 62]. To each system described in any of these formalisms one can associate a transition system or automaton consisting of (1) a set of states, 2) a set of initial states, 3) a set of discrete actions, 4) a set of discrete steps s Gamma s asserting that from state s the system can ....

....believe that timed automata, defined in this way, provide an excellent basis for defining and studying behavioral preorders and simulation proof techniques for timing based systems. Since timed automata can be viewed as an underlying semantic domain for any of the models, languages and logics of [2, 5, 7, 8, 9, 11, 14, 17, 20, 25, 26, 27, 48, 50, 52, 54, 61, 62], all the results that we obtain for timed automata carry over directly to those settings. For convenience, we use R as our domain of times in this paper. The need for densetime models has been well discussed in [4] However, for the purpose of generality we could have parameterized our timed ....

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [10], pages 401--415.

....quantitative time, because time constraints of such systems are frequently altered depending on implementations. In such cases, we must guarantee that the system s essential behaviour would not be changed. In the latest years many languages have been proposed to describe real time prop erties [5 10]. For example, timed extensions of CCS[5 7] introduced several primi tive operators such as delay and timeout operators to describe real time properties. However, in these languages, even describing a simple time constraint that some action has to be done within a given time interval yields to a ....

....of such systems are frequently altered depending on implementations. In such cases, we must guarantee that the system s essential behaviour would not be changed. In the latest years many languages have been proposed to describe real time prop erties [5 10] For example, timed extensions of CCS[5 7], introduced several primi tive operators such as delay and timeout operators to describe real time properties. However, in these languages, even describing a simple time constraint that some action has to be done within a given time interval yields to a complicated descrip tion. Although ....

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F. Moller and C. Tofts, "A temporal calculus of communicating systems," in Proc. of CONCUR '90, vol. 458 of Lecture Notes in Computer Science, pp. 401-415, Springer-Verlag, 1990.

....tasks are critical, in the sense that they must be executed urgently once they become enabled. Thus, in the last years several extensions of the classical models to describe concurrent systems have been defined in order to incorporate this factor: we have timed extensions of CSP [17, 13, 19] CCS [11], and LOTOS [15] Bolognesi and Lucidi [2] have defined another timed extension of LOTOS, which includes an operator for the specification of urgent interactions. Hansson and Jonsson have defined another timed and probabilistic extension of CCS [7, 6] by including a time out operator. In fact, ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. Proceedings CONCUR 90, Lecture Notes in Computer Science, (458):401--415, 1990.

....systems. In recent years process algebras which involve time have been proposed to fulfill the need for formalisms able to deal with quantitative time aspects of systems. The option to represent time by non negative reals and to have time stamps on actions is taken into account in [2] for ACP, in [9] for CCS and in [1] for CSP. Another option is to divide time into slices, thus giving the possibility to use an implicit or explicit time stamping mechanism that provides each action with the index of the time slice in which it occurs. This has been developed for the case of ACP in [3] Frame ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. In CONCUR'90, LNCS. Springer, 1990.

....are critical, in the sense that they must be executed urgently once they become enabled. Thus, in the last years several extensions of the classical models to describe concurrent systems have been de ned in order to incorporate this factor: we have timed extensions of CSP [RR88,Ort90,Sch95] CCS [MT90], and LOTOS [QAdF89] Bolognesi and Lucidi [BL91] have de ned another timed extension of LOTOS, which includes an operator for the speci cation of urgent interactions. Hansson and Jonsson have de ned another timed and probabilistic extension of CCS [HJ90,Han92] by including a time out ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. Proceedings CONCUR 90, Lecture Notes in Computer Science, (458):401{ 415, 1990.

....theory has recently been devoted to the development of extensions of standard process algebras like CCS [16] CSP [11] and ACP [3] with constructs allowing for the modelling of timing aspects in the behaviour of processes. By now, most process algebras have a timed counterpart (see, e.g. [1, 6, 18, 21]) and the development of results and techniques for these languages is becoming comparable with that for the standard process description languages. For example, complete axiomatizations of behavioural On leave from School of Cognitive and Computing Sciences, University of Sussex, Brighton BN1 ....

....Research in Computer Science, Centre of the Danish National Research Foundation. Supported by SERC project GR H 16537. Additional funding was received from EC BRA 7166 concur2. Email: alanje cogs.susx.ac.uk. 1 congruences for subsets of timed process algebras have been presented in, e.g. [10, 14, 18, 22] showing that behavioural congruences which deal with timing considerations are as mathematically tractable as the standard untimed ones. Two of the most beautiful results in the theory of process algebras are the complete axiomatizations of strong bisimulation equivalence and observational ....

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [2], pages 401--415.

....using predicates [9] However, in the literature SOS de nitions are often decorated with predicates and or negative premises. For example, predicates are used to express matters like (un)successful termination, convergence, divergence [3] enabledness [14] maximal delay, and side conditions [42]. Negative premises are used to describe, e.g. deadlock detection [38] sequencing [17] priorities [7, 21] probabilistic behaviour [39] urgency [19] and various real [37] and discrete time [6, 35] settings. Since predicates and negative premises are so pervasive, and often lead to cleaner ....

F. Moller and C. Tofts, A temporal calculus of communicating systems, in Baeten and Klop [8], pp. 401-415.

....discussed below. 3.4.3 Timed extensions of process algebras Considerable e#ort has been put into developing process algebras which explicitly represent quantitative time. The timed process algebras are generally derived as extensions of untimed process algebras(see Section 2. 5) Thus Temporal CCS [48] and Timed CCS [68] derive from CCS [46] TCSP [53] from CSP [56] U LOTOS [8] from LOTOS [6] and TPL [30] is derived from Hennessy s Acceptance Trees [28] In Section 3.4.1 the distinction between discrete and dense (ie infinitely divisible) representations of time was noted. This distinction is ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [3], pages 401--415.

....nature. Research on all these quantitative extensions of process algebras started around the same time. 2.1 Timed process algebras Timed extensions of process algebras have received considerable attention in the last decade. To mention a few, extensions of languages like ACP [5] CSP [92] CCS [80,104] and LOTOS [15,75] have been defined. The main idea of these calculi is to extend the language with a timed prefix like (t) P which denotes that process P is reached after a delay of t time units. Both discrete time and real time variants are considered, depending on the domain of t. A main ....

....by a (continuous) random variable, # say, such that Prob(# # t) equals 1 e #t for positive t, and equals zero otherwise. The prefix (#) P can be considered as the probabilistic version of the deterministic timed prefix (t) P that typically occurs in timed process algebras, like in TCCS [80] or in Timed CSP [92] In general, the 14 term P i#I (# i ) P i o#ers a probabilistic choice among the processes P i . The precise meaning of this construct is defined below. Notation: if I consists of two elements we use binary choice, denoted . 4.2 Semantics The structured operational ....

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.C.M. Baeten and J-W. Klop, eds, Concur'90: Theories of Concurrency -- Unification and Extension, LNCS 458, pages 401--415, 1990.

....of actions at the same point in time. We introduce different equivalence relations based on bisimulation. 1 Introduction Real time models are used to model time dependent physical problems. The common approach is to restrict action occurrences to closed, more precisely to left closed intervals [RR88, Sch00, MT90, Wan90, Mur92, FZ94, CL96, LL97]. Contrary to this, timed automata [AD94] and some process algebras [BB91, Klu91, Dan91, Che92, Jef92] allow actions to occur in open intervals in order to increase their expressive power. Another important property of timed process algebras is the maximal progress assumption, i.e. an action must ....

....we only consider weakly guarded expressions on the left hand side of . For further details see Remark 7. We separate in the transition system the performing of actions and the passing of time. To define the transition rules we use Moller Tofts maximal delay times of processes before any action [MT90]. Since we consider also right open intervals we have to change the range of the function. Therefore, we define T 0 to be T Thetaf ; g with the lexicographical order, where is smaller than . Furthermore, T c be T 0 with the additional least element 0 and the additional greatest element ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. LNCS, 458:401--415, 1990.

....parallel composition is 1=n, with n natural number, then each action of P takes exactly n time units to be executed, instead of n time units on average. With a standard approach based on a synchronous parallel composition, where parallel processes are executed in synchronous locksteps (see, e.g. [21,27,24,31,17]) exact advancing speeds could be modeled as follows. Called n P the duration of the actions of a process P (number of time units taken to execute each action of P ) we compute the greater common divisor div of the set of durations n P where P is a process composing the system. Then for each ....

F. Moller, C. Tofts, \A Temporal Calculus of Communicating Systems", in Proc. of 1st Int. Conf. on Concurrency Theory, LNCS 458:401-415, SpringerVerlag, 1990

....But we could not simply change the workcells to allow overbooking of tentative jobs, because we would then accept contracts that were not feasible. 5. FORMALIZATION OF THE PROBLEM We now model a simplified version of our scenario using a Temporal Calculus of Communicating Systems (TCCS) 5][6] (one of several that exist by the same acronym) This model is then fed into the Edinburgh Concurrency Workbench [2] CWB) version 7.1 for analysis. For a minimal introduction to TCCS notation, please refer to the Appendix of this paper. We originally modeled the complete scenario with three ....

....testing and debugging tools and facilitate effective analysis of coordination problems. 8. APPENDIX: TCCS NOTATION It is not possible to capture accurate and full semantics for TCCS in the space available. For a complete and formal introduction, please refer to the cited references [5][6]. Table 2. TCCS notation guide Example Semantics j C cfp , Send this message to a receiving process. Not possible to proceed if no such process exists. j C cfp , Receive this message from a sending process. Not possible to proceed if no such process exists. Y X . Do X, then do Y. Y X Do X ....

Moller, F., and Tofts, C. A temporal calculus of communicating systems. Lecture Notes in Computer Science #458, Springer-Verlag, 1990, 401-415.

....timed automata, the notion of time is introduced by a set of clock variables. Vertices represent control information of the systems, and edges indicate how the systems evolve by making transitions. Edges and vertices can be labeled by conditions on the clocks variables. Real time process algebras [64, 87, 74, 68, 61] have been extensively studied as speci cation formalisms for real time systems. Process algebras are textual languages based on algebraic theory. In process algebras, components of the systems are represented by processes. Operators are de ned to construct more complicated processes from simple ....

F. Moller and C. M. N. Tofts. A temporal calculus of communicating systems. In CONCUR'90 Theories of Concurrency: Unication and Extension (LNCS 458), pages 401-415. Springer-Verlag, 1990.

....for future research are given in Section 8. 2 BASIC IDEAS AND RELATED RESEARCH The process calculus PRTCCS developed in this paper should be able to represent the basic concepts of POOSL. POOSL offers real time, asynchronous concurrency and pair wise synchronous communication. Just as the TCCS (Moller and Tofts 1990) algebra, POOSL uses a two phase execution model. The state of a system can change either by asynchronously executing atomic actions or by letting the time pass synchronously. The execution of actions does not take any time. In literature a lot of proposals for extending non real time process ....

....The work is not in the context of performance analysis but it focuses on testing semantics and on probabilities with which a process can pass a test. Rodrguez et al..1997) uses a discrete time model. The operational characterization of time follows the approach applied in TCCS by Moller and Tofts (Moller and Tofts 1990. The operational semantics of POOSL (Geilen and Voeten 1997) also follows this approach. A disadvantage of this, however, is that it does not offer a constructive method for building a discrete time Markov chain. The problem is that due to the time closure property (Rodrguez et al..1997) the ....

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Moller, F. and C.Tofts. 1990. "A Temporal Calculus of Communicating Systems." In Proceedings of CONCUR'90 (Amsterdam Aug.26--29). Springer, Berlin, 401--415.

.... a notion of discrete time similar to [NS90] During the generalisation of this algebraic approach to continuous time we realised difficulties in developing an expansion theorem and in completeness questions, what seems to be a general problem, as is also pointed out for instance in [NS91] and in [MT90], respectively. This brought us to consider the present abstract description of real time constraints using predicates, what fits together with the fact that SL 0 is provided with a predicative semantics. Some results from [Sch91] can be confirmed also in the present model, for instance the ....

F.Moller, C.Tofts. A temporal calculus of communicating systems. CONCUR 1990, LNCS458.

....to be used as a system level modelling language. The POOSL language combines a data part with a process part. The data part is based upon the concepts of traditional sequential object oriented programming languages such as Smalltalk [5] C [6] and Eiffel [7] The process part is based on TCCS [11], the timed extension of the CCS process algebra [3] 4] Modelling techniques based on such classical process algebras have proven to be very useful to describe complex realtime systems and to verify their qualitative (correctness) properties. Unfortunately, these techniques do not support the ....

F. Moller and C. Tofts, A Temporal Calculus of Communicating Systems, in Proceedings of CONCUR'90, J.C.M. Baeten and J.W. Klop, Eds., Berlin, pp. 401--415, Springer-Verlag, 1990.

....In this way it is defined what actions a process may perform. This description however, does not tell us anything about when these actions are being performed. In order to add such timing information, some existing process algebras have been extended with a notion of time, such as TeCCS [8], TCSP [9] ATP [10] and ACP # [11] IV. Timing concepts In this section, concepts of time and their impact on the implementation of the real time semantics are discussed. Abstraction and non determinism. Models are abstractions of reality. With the information lost in the abstraction, ....

F. Moller and C. Tofts, "A temporal calculus of communicating systems," in CONCUR'90 Theories of Concurrency: Unification and Extension Proc. Amsterdam, The Netherlands 27-30 Aug. 1990, Lecture Notes in Computer Science V.458, J.C.M. Baeten and J.W. Klop, Eds., Berlin, 1990, pp. 401--415, Springer Verlag.

....address this problem in this paper. In the untimed setting, bisimulation equivalences have been reasonably successful as notions of implementation between transition systems [6, 34] Consequently, bisimulation equivalences have also been proposed as implementation relations for the timed setting [4, 23, 35, 38, 46]. However, we do not believe that bisimulations will turn out to be very useful as implementation relations in the timed case. The problem is that they do not allow one to abstract in specifications from the often very complex timing behavior of implementations (see Chapter 10 of [23] for an ....

....that can block the passage of time, and a RATE operation that can change the speed of its argument. On the other hand, there are several operators that have been proposed in the literature that do not fit our format of action transducers, in particular, the CCS style choice operation present in [4, 35, 38, 46]. This operation cannot be expressed as a timed action transducer because the timed trace inclusion relation is not substitutive with respect to it. We briefly consider the design of an appropriate language of operators for describing timingbased systems. Such a language should consist of a small ....

[Article contains additional citation context not shown here]

F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [5], pages 401--415.

....by the guaranteed progress of time. We refer the reader to [AH89] Ost90] AL91] and the survey in [AH92] for additional logics, models, and approaches to the verification of real time systems. In the process algebra school, some of the representative approaches to real time are [NSY92] MT90] and many others are listed in [Sif91] The paper is organized as follows. In Section 2, we present the real time computational model of clocked transition systems (cts) In Section 3, we show how programs augmented with timing bounds for the execution of statements can be represented as clocked ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.C.M. Baeten and J.W. Klop, editors, Proceedings of Concur'90, volume 458 of Lect. Notes in Comp. Sci., pages 401--415. Springer-Verlag, 1990. 74

....timed transition systems Note: Work carried out under project SEN2.1 Process Specification and Analysis . 1 Introduction Time often plays a crucial role in process behaviour. For this reason, process algebras such as CCS [18] CSP [15] and ACP [4, 5] have been extended with some notion of time [19, 20, 1, 2]. In general, these approaches tend to be restricted to the syntax and semantics of these formalisms. Disappointingly, protocol verification in timed process algebras has proved to be a complex task. In this paper, we propose a method that will make larger timed verifications feasible. The method ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. In J. C. M. Baeten and J. W. Klop, editors, Proceedings of CONCUR'90, volume 458 of Lecture Notes in Computer Science, pages 401--415. Springer-Verlag, 1990.

....In physical terms this can be seen as deciding the starting time of each component. In the literature, much attention has been given to the the first configuration step, both at the architectural level and at the specification level [20, 15, 17, 4, 18] and to modeling time in various formalisms [7, 14, 21, 19, 9, 13]. In this paper we present a framework in which it is possible to specify the architecture of a system as a network of (parallel) components, each one with its own local clock. Thus, the configuration of the behavioral part is achieved by putting the components in parallel and let them communicate ....

....the video stream is played out. In presence of synchronization, instead, it is not always the case that faster components imply faster systems. Consider ( 0 ) SensorD j 0 ) SensorA j 0 ) SensorE j 0 ) ContrD j 0 ) ContrA j 0 ) ContrE j 0 ) Pump)nA) 0; the initial state of System 1 . see [21]) Processes with time stops may cause the deadlock of all processes which are in parallel composition or in alternative composition with the process itself. Thus, the Mine Pump System and the Lip one, are deadlock free in usual sense; i.e. they never reach states where no action can be ....

[Article contains additional citation context not shown here]

Moller,F., Tofts,C.: A Temporal Calculus of Communicating Systems. Proc. of CONCUR'90, LNCS 459, Springer-Verlag (1990), 401-415.

.... a simple process algebra [20, 15, 18] Local clocks are modeled as higher order terms in a given signature, and unification is used to define the common clock [16] Then an operational semantics defines which transitions a process can perform and which transitions let time to elapse similarly to [7, 14, 21, 10]. This work has been partially funded by CNR, Progetto: Metodologie e strumenti di analisi, verifica e validazione per sistemi software affidabili In particular we specify the architecture of a system as a network of (parallel) components, each one with its own local clock. This means that, ....

....applications to telecommunication systems. The system description language we consider implements several ideas from classic timed process description languages. The idea of using local clocks is taken from [7, 14, 10] the view of system activities as instantaneous events is taken from [21] (and related works, see references therein) The rational for this choice is that since we are concerned with the static analysis of behavioral aspects of systems obtained by assembling together components running at (possibly) different speed we prefer to abstract from events duration while ....

[Article contains additional citation context not shown here]

Moller,F., Tofts,C.: A Temporal Calculus of Communicating Systems. Proc. of CONCUR'90, LNCS 459, Springer-Verlag (1990), 401-415.

....tasks are critical, in the sense that they must be executed urgently once they become enabled. Thus, in the last years several extensions of the classical models to describe concurrent systems have been de ned in order to incorporate this factor: we have timed extensions of CSP [17, 13, 19] CCS [11], and LOTOS [15] Bolognesi and Lucidi [2] have de ned another timed extension of LOTOS, which includes an operator for the speci cation of urgent interactions. Hansson and Jonsson have de ned another timed and probabilistic extension of CCS [7, 6] by including a time out operator. In fact, there ....

F. Moller and C. Tofts, A temporal calculus of communicating systems, Proceedings CONCUR 90, Lecture Notes in Computer Science (1990), no. 458, 401-415.

....(bi)simulation. AMS SUBJECT CLASSIFICATION (1991) 68Q05, 68Q55, 68Q60, 68Q75, 03E25. CR SUBJECT CLASSIFICATION (1991) D.2.4, D.3.1, F.1.1, F.3.2. KEYWORDS PHRASES: Timed transition system, concurrency theory, simulation, bisimulation, trajectory. 1 Introduction Timed transition systems [MoT90, Wan91] are commonly used in the specification of time critical systems. They describe a system in terms of the states it can be in, and circumstances under which it can move from one state to the next, either by allowing time to pass or by performing some transition. There are a Alan Jeffrey: ....

....with are image finite: only finitely many results are possible from any state through any particular (delay or action) transition. As well as the transition systems mentioned above, these include a number of algebras using the reals as the underlying time domain: the three versions of Timed CCS [MoT90, Wan91, Che91], Timed ACP [BaB91] APA [Jef91] and a different version of timed LOTOS [QAF89] These are all additive, so it follows that they are trajectoried. Timed CSP [Sch92] and PARTY [Ho 92] are not image finite; they both allow infinite choice. However, they are both forward and backward deterministic ....

F. Moller and C. Tofts, A temporal calculus of communicating systems, pp 401--415, LNCS 458, 1990.

....they cannot represent the actual time between events, only the ordering in time of these events. Trying to build on their success, and to provide the basis for a formal method for real time systems, many timed process algebras have been developed, including extensions to existing algebras [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16] for reviews see [17, 18] In section 2 we argue that, while useful, timed process algebras cannot as easily be used as broad spectrum languages (in the way that CCS and Z [19] can be) and that a different approach needs to be taken. The focus of the rest of the paper is then made clear in ....

F Moller and C Tofts. A temporal calculus of communicating systems. Technical Report ECS-LFCS-89-104, Edinburgh University, December 1989.

....used for timed process algebras can be often viewed as extensions to the languages for untimed process algebras by adding some specific constructs or by assuming that in some cases prefixing by an action may delay. As an example consider timed crossing in the language of TCCS by Moller and Tofts [8]: Rail df = train j 1 0 :green j 1 0 :tcross j 1 0 :red j 1 0 :Rail Road df = car j 1 0 :up j 1 0 :down j 1 0 :Road Signal df = green j 1 0 :red j 1 0 :Signal up j 1 0 :down j 1 0 :Signal Crossing df = Raod j Rail j Signal)nfgreen, red, up, downg 3 The meaning ....

Moller, F. and Tofts, C.: A Temporal Calculus of Communicating Systems. University of Edinburgh, Report No. LFCS-89-104, 1989.

....implementation that cannot be refined from a specification, FDR automates the analysis required to determine the action trace that causes the implementation to fail to refine the specification. CWB[1] Concurrency Workbench) automates the analysis of processes defined using CCS[18] and Timed CCS[19]. Basic functions provided include analysis of the state space of a given process, checking of various semantic equivalences and preorders, the ability to define propositions in modal logic and check whether a given process satisfies such propositions, interactive execution of process ....

F. Moller and C. Tofts. A Temporal Calculus of Communicating Systems. In Proc. of CONCUR '90, pages 401--415. LNCS 458, Springer Verlag, August 1990.

....used widely in specifying and verifying concurrent systems. To expand their usefulness to real time systems, several real time process algebras have been developed by adding the notion of time and including a set of timing operators; e.g. Davies and Schneider (1989) Hennessy and Regan (1990) Moller and Tofts (1990) Yi (1991), and Nicollin and Sifakis (1994) The most salient aspect of process algebras is that they support the modular specification and verification of a system. This is due to the algebraic laws that form a compositional proof system, and thus, it is possible to verify the whole system by reasoning ....

Moller, F., and Tofts, C. A Temporal Calculus of Communicating Systems, in Proceedings, CONCUR '90, pp 401--415. Lecture Notes in Comput. Sci. Vol. 458, Springer-Verlag, Berlin. Nicollin, X., and Sifakis, J. (1991), "The Algebra of Timed Processes ATP: Theory and Application," Technical Report RT-C26, Institut National Polytechnique De Grenoble.

....the only case in which an event and a timed action are comparable under OE. That is, when p 0 in an event ( p) we let the event preempt any timed action. This, in effect, makes synchronization take precedence over the passage of time and is similar to the notion of maximum progress found in [26, 46, 53]. The case where p = 0 is treated differently. It is meant to allow the specification of nondeterministic behaviors, e.g. to model an environment that can interact with a process at any time rather than at the earliest possible time. March 22, 1995 14 Note that the preemption relation is ....

....untimed CCS. In most cases, the parallel and choice operators are patient with regard to time, that is, if the two arguments of the operator can let time elapse the combined process can let time elapse without committing to a particular behavior. Another common notion is that of maximal progress [26, 46, 53] by which if two parallel processes can communicate, this communication occurs as early as possible. Temporal CCS (or TCCS) 46] which CCS not only with time passing actions but also with a weak choice operator. Both operators are patient with regard to the passage of time, but while the choice ....

[Article contains additional citation context not shown here]

F. Moller and C. Tofts. A Temporal Calculus of Communicating Systems. In Proc. of CONCUR '90, pages 401--415. LNCS 458, Springer Verlag, August 1990.

....This is often called the maximal progress assumption. Our format is inspired by TPL [HeR91] which was in turn influenced by [Phi89] It is a subformat of SF, where we make a restriction on the s rules. Apart from TPL, other timed process algebras have been proposed in [ReR88] BaB91] NRSV90] [MoT90], Wan90] among others. DEFINITION 4.1 (Timed format) Let a language definition S have action set A containing special actions t, s. Then S is in timed format (TF) if it is in SF and satisfies the following further conditions: 1) s may not appear in either the premises or conclusion of a DeS ....

F. Moller and C. Tofts. A temporal calculus of communicating systems. CONCUR'90. LNCS 458 (401-415). Springer, 1990. 11/7/97 13

....are assumed to be instantaneous and only relative timing is represented via the traces of the process. Time may be represented explicitly in a process algebra by allowing an agent to witness periods of delay, of specified lengths, in addition to witnessing actions, as in Temporal CCS (TCCS) [49]. In TCCS actions are still assumed to be instantaneous, and the time domain is taken to be the natural numbers. The language is given an operational semantics with two different types of transition: action transitions and time transitions. 2.1.2 Probabilistic Process Algebras Process algebras ....

F. Moller and C. Tofts. A Temporal Calculus of Communicating Systems. In CONCUR 90, pages 33--56. Springer, Berlin, LNCS 458, 1990.

....some behaviours that are unrealisable in practice. However every possible failure in the original M will be captured by the translation M . A more refined target process algebra should be used when errors unrealisable in M occur in M . Richer process algebras can be used to account for timing [29] or probabilistic [42, 43] behaviour of systems, but their descriptions are usually much more complicated. In most cases, systems failures result from underlying interaction errors rather than specific problems and can be captured in the simpler process algebras we espouse. 1 The Edinburgh CWB ....

F. Moller and C. Tofts. A Temporal Calculus of Communicating Systems. In J. W. Klop J. C. M. Baeten, editor, CONCUR '90, number 458 in LNCS. Springer-Verlag, 1990.

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F. Moller and C. Tofts. A temporal calculus of communicating systems. In Baeten and Klop [BK90], 401--415. (pp 16, 17)

No context found.

F Moller and C Tofts. A temporal calculus of communicating systems. Technical Report ECS-LFCS-89-104, Edinburgh University, December 1989.

No context found.

F. Moller and C. Tofts. A temporal calculus of communicating systems. In J.C.M. Baeten and J.W. Klop, editors, Proceedings CONCUR 90, Amsterdam, pages 401-- 415, Springer-Verlag, 1990.

No context found.

F. Moller, C. Tofts, A temporal calculus of communicating systems, in: J.C.M. Baeten, J.W. Klop (Eds.), CONCUR'90, Lecture Notes in Computer Science, vol. 458, Springer, Berlin, 1990, pp. 401--415.

No context found.

F. Moller, C. Tofts, A temporal calculus of communicating systems, in: Proceedings of the CONCUR'90, 1990, pp. 401--415.

No context found.

F Moller and C Tofts. A temporal calculus of communicating systems. Technical Report ECS-LFCS89 -104, Edinburgh University, December 1989.

No context found.

F. Moller, C. Tofts, A temporal calculus of communicating systems, in: J.C.M. Baeten, J-W. Klop (Eds.), Concur'90: Theories of Concurrency --- Uni#cation and Extension, Lecture Notes in Computer Science, vol. 458, Springer, Berlin, 1990, pp. 401-- 415.

No context found.

F. Moller, C. Tofts, A Temporal Calculus of Communicating Systems, in: Proc. of CONCUR'90, Lecture Notes in Computer Science, Vol. 459, (Springer, Berlin, 1990), 401-415.

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