Nicollin, X., Sifakis, J.: The algebra of timed processes ATP: theory and application, Information and Computation, Vol. 114(1), pp. 131-178, (1994).  Home/Search   Document Details and Download   Summary   Related Articles   Check

....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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X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114(1):131--178, 1994.

....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. Unfortunately, the conventional process algebras are not particularly suited for ....

....other (static) real time algebras, this simplifies the for malisation. Discrete time: We will use the set of natural num bers as the time domain, i.e. time is discrete and is strictly increasing. We can view each passing of a time unit as a clock tick and we model it as an explicit event as in [NS94] This is somewhat contrary to the popular way of thinking that the passage of time is associated with observing a succession of distinct, observable events [L 8] By treating time passing as an explicit event, we can let time pass without any other actions oc curing. See also the time ....

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Xavier Nicollin, Joseph Sifakis, "The Alge- bra of Timed Processes ATP: Theory and Application ", Information and Computation 114(1):131- 178, 1994.

....in Section 0.3 have been adapted to real time. For automated theorem proving, the applicability for timed settings has been explored, e.g. in [Sha93] For process algebras, a number of calculi addressing time as a primitive exist. Examples for this are Timed CSP [RR88] TCCS [Yi90] and ATP [NS94] For stepwise refinement, time settings have been explored, e.g. in [SZJ94] For abstract interpretation, approximation of real time safety properties can be formulated in the have been formulated in this framework [WT94, DT98] An approach to approximate also liveness is presented in Chapter ....

Xavier Nicollin and Joseph Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Information and Computation, 114(1):131--178, 1994. 14

....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 ....

[Article contains additional citation context not shown here]

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114(1):131--178, 1994.

.... a visible action then A is interrupted and B continues to run) They also include some timed operations such as the timed CSP timeout [6, 35] i.e. A is started; if A does not perform a visible action by real time d, then A is interrupted and B is started) and the ATP execution delay operator [31]. The admissible timed trace inclusion relation (more precisely, a variant of it that includes certain kinds of finite timed traces as well) is shown to be substitutive with respect to all of these operations. 3 Simulations for Timed Automata In this section, I introduce the basic types of ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application, November 1991. Technical Report RT-C26, LGI-IMAG (revised version).

....steps representing the execution of actions and the passage of time to the next time slice, respectively. Equipped with a root marker and optionally with termination markers, timed frames make up the transition systems that match with the twophase functioning scheme for modeling timed processes [10]. There is a well developed tradition of thinking about transition systems from modal logic (for an overview of modal formalisms for describing transition systems, see e.g. 11] Process algebra studies transition systems at a more abstract level: transition systems modulo an appropriate process ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....this paper well. However, it is certainly not the only one possible, and several ones have been proposed in the literature (see [4] for a series of examples) Complete axiomatizations of behavioural equivalences for several timed process algebras have been presented in the literature; see, e.g. [7, 10, 14, 18, 19, 22] for examples of such results. With the notable exception of the one presented in [10] all the aforementioned axiomatizations are restricted to recursion free processes. Hennessy and Regan s axiomatization of their behavioural precongruence over the language TPL includes an infinitary conditional ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application (revised version). Technical Report RT-C26, LGI-IMAG, Grenoble, France, November 1991.

....is a great demand for formal methods applicable to real time systems. Developing formal methods for the design and analysis of real time systems is a very active area of current research. Several different formalisms have been proposed. These include timed Petri Nets [4] timed process algebras [9, 10, 6], real time temporal logics [2, 5] and timed automata [1] Moreover, there is a pressing need to develop efficient tools to be embedded in a real time software development process. Timed algebras are process algebras extended with a set of constructs to express timing requirements. They have ....

....software development process. Timed algebras are process algebras extended with a set of constructs to express timing requirements. They have formal semantics, given in terms of transition systems or sets of traces, and are a quite adequate to describe the behavior of real time systems. ATP [6] is a timed process algebra which introduces a mechanism to delay the execution of an action and provides two language constructs, namely timeouts and watchdogs, to express timing constraints. Proc. XVIII Conf. Latinoamericana de Inform atica, PANEL 92, pages 1243 1250, August 1992 2 Timed ....

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X. Nicollin and J. Sifakis. The algebra of timed processes ATP: theory and application. Technical Report RT-C26, LGI-IMAG, France, December 1990. To appear in Information and Computation.

.... The approach is sufficiently accurate in many practical cases (see e.g. 6] reduces the complexity of the system behaviour under time constraints, defines a natural simulation (or interpretation) scheme that usually is assumed in simulation languages, allows for some algebraization (see e.g. [11]) and axiomatization (see e.g. 1] facilitating verification. Still it is a simplifying approach and the zero duration of actions may cause some strange behaviour in which time does not progress, despite millions actions executed, because always there is one more to perform. 3 The aim of this ....

Nicollin, X., Sifakis, J., The Algebra of Timed Processes ATP: Theory and Application, Internal Report, IMAG, Grenoble, 1990 (also see [9])

....on strong bisimulation are defined and axiomatizations developed. Process algebras for real time systems have also been developed. Generally speaking, these theories introduce special time passing actions, with all other actions being viewed as instantaneous. The Algebra of Timed Processes [37] pioneered this approach, with useful variants being proposed in [30] Another area of ongoing research involves the incorporation of probabilistic behavior into systems, with a view toward providing a theory in which quality of service statements can be made. One strand of this research augments ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114(1):131--178, October 1994.

....is possible, but this trick does not contribute to comprehensibility. In many applications of TSSs, it is in addition necessary to have support for many sortedness or variable binding operators. Many sortedness is found, for example, in process algebras with timing (see e.g. 4] 11] and [30]) Examples of variable binding operators are the integration operator R of real time ACP [4] and the recursion operator of CSP [25] and CCS [28] Using transition rules to cope with many sortedness is unpractical and obscures the fact that it is a static matter. Variable binding operators can ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

....time. For simplicity we ignore here the state part and thus arrive at a specification language, where the trace part of SL 0 is augmented by time predicates. In a previous paper ( Sch91] we have presented a purely algebraic approach, how to extend SL 0 by 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 ....

....tim dur(a) Then ( re 1 ; G 1 ) re m ; Gm ) tp 1 ; tp n ; tp a ; where tp a ; stands for all tp a with a 2 A, specifies the same process with attributed duration, provided it runs on one processor. 3. 4 A login procedure We present our version of the login procedure from [NS90], NSY91] To start the procedure L, the system sends a login prompt prompt. After this event, the user has l time units to enter a valid login response val to successfully finish the task and to start a session phase Sess. When the user supplies an invalid response nonval, or when time l elapsed, ....

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X.Nicollin, J.Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Report RT-C26, Projet SPECTRE, Universit'e de Grenoble. 14

....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, non determinism is ....

X. Nicollin and J. Sifakis, "The algebra of timed processes, ATP: theory and application," Information and Computation, vol. 144, no. 1, pp. 131--78, 1994.

....such as the role of durations and forcing of events. Models of timed discrete event systems that have been proposed include discrete time systems [7] timed automata proposed by R. Alur and D. Dill [1, 3] temporal logic [36] and timed process algebras developed by J. Sifakis and co workers [32, 33, 34]. Control of timed discrete event systems is treated in [7, 20, 29, 36, 46] of which the work by G. Hoffmann and H. Wong Toi is of particular interest. An application to specification and design of a telephone exchange is presented in [24] A hybrid system is a mathematical model of a phenomenon ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and applications. Information and Computation, 114:131--178, 1994.

....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]

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114(1):131--178, 1994.

....Timed frames [7] cover virtually all kinds of transition systems for the discrete time case. Timed frames are in essence the two phase transition systems considered in [6] as the objects underlying discrete time process algebras. They underlie well known discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5] Two phase transition systems are closely related to the real time transition systems that underlie the real time extension of ACP presented in [3] In [4] it is shown that the model of the discrete time extension of ACP based on two phase ....

....scale. It means that the discrete time points just divide real time into time slices and, although actions and state changes take place in real time, only the time slices in which actions and state changes take place are considered to be of importance. Discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5] o#er exactly this abstraction. Naturally, it is in accordance with the intended meaning of a time step the passage of time to the next time slice for it derives this meaning from its use in these discrete time process algebras. ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....The domain of timed strings corresponding to the transitions that may be performed will be interval finite, and so these transition systems will be trajectoried. These include one of the versions of timed LOTOS [BoL92] the Temporal Process Language of [HeR91] the Algebra of Timed Processes ATP [NiS90], the process algebra described in [Ort92] and the algebra for time and probabilities [Han91] Also, the transition systems discussed in [ClZ92] are required to be image finite, which is enough to ensure that they are trajectoried. The majority of timed transition systems which the authors are ....

X. Nicollin and J. Sifakis, The algebra of timed processes ATP: theory and application, RT-C26, Project SPECTRE, Laboratoire de Genie Informatique de Grenoble, 1991 .

....Stony Brook, New York, U.S.A, August 1992 1 acterized axiomatically and we present axiom systems for time deterministic and time additive transition systems. In section 2, we recall basic facts about timed transition systems. For detailed explanation we refere to the work by Nicollin and Sifakis [5, 7]. Section 3 defines the properties of timed transition systems under consideration. Then, section 4 extends propositional modal logic and modal calculus with an additional temporal operator with the intention to capture quantitative properties of timed systems. In section 5, we give the ....

Nicollin, X. and Sifakis, J.: The algebra of timed processes ATP: Theory and Application. Technical Report RT-C26, Laboratoire de G'enie Informatique de Grenoble, 1990.

....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 about its parts. The reasoning on ....

....the timed failure model. Because of the dense time domain, the language is no longer axiomatizable. For verification, Davies and Schneider (1989) developed a proof system that can be used to show that P satf , where the formula f is in timed failure trace logic 7. 3 ACP Based Process Algebras Nicollin and Sifakis (1991, 1994) present the Algebra of Timed Processes (ATP) which extends a combination of CCS and ACP with a unique feature, the unit delay operator (b Gammac) The process bP c(Q) behaves as P if P starts executing before the next time unit; otherwise, after the delay of one time unit, it behaves as Q. It is ....

Nicollin, X., and Sifakis, J. (1994), The Algebra of Timed Processes ATP: Theory and Application, Information and Computation 114(1), 131--178.

....such as the role of durations and forcing of events. Models of timed discrete event systems that have been proposed include discrete time systems [7] timed automata proposed by R. Alur and D. Dill [1, 3] temporal logic [36] and timed process algebras developed by J. Sifakis and co workers [32, 33, 34]. Control of timed discrete event systems is treated in [7, 20, 29, 36, 46] of which the work by G. Hoffmann and H. Wong Toi is of particular interest. An application to specification and design of a telephone exchange is presented in [24] A hybrid system is a mathematical model of a phenomenon ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and applications. Information and Computation, 114:131--178, 1994.

....in the syntax, while in our case it is implicit. Nevertheless, our treatment of compositionality was inspired by it. In [8] it is shown that some equivalence relations such as ready and failure equivalence are no longer congruences when priorities are introduced. Algebra of Timed Processes or ATP [47] is another process algebra with discrete time. The execution model is similar to ours in that processes evolve in two phase steps; in the first phase, all instantaneous actions are executed in an asynchronous (interleaved) manner with some possible communication. When no more component can ....

X. Nicollin and J. Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Technical Report RT-C26, Institut National Polytechnique De Grenoble, November 1991.

....The domain of timed strings corresponding to the transitions that may be performed will be interval finite, and so these transition systems will be trajectoried. These include one of the versions of timed lotos [BoL92] the Temporal Process Language of [HeR91] the Algebra of Timed Processes ATP [NiS90], the process algebra described in [Ort92] and the algebra for time and probabilities [Han91] Also, the transition systems discussed in [ClZ92] are required to be image finite, which is enough to ensure that they are trajectoried. The majority of timed transition systems which the authors are ....

X. Nicollin and J. Sifakis, The algebra of timed processes ATP: theory and application, RT-C26, Project SPECTRE, Laboratoire de G'enie Informatique de Grenoble, 1991 .

....time stamping of actions can be obtained. The real time versions of ACP presented in [6] unlike those presented in [2] and [3] do not exclude the possibility of two or more actions to be performed consecutively at the same point in time. That is, they include urgent actions, similar to ATP [19] and the different versions of CCS with timing [11, 18, 21] This feature seems to be essential to obtain simple and natural embeddings of discrete time versions as well as useful in practice when describing and analyzing systems in which actions occur that are entirely independent. This is, for ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....without value parameter, for function without result (x 5.5.1, p. 52) for non exiting processes (x 6.7.1, p. 64) and for typing expressions and statements. 4.3.8 The time type The case of type time is special in Lotos NT. It denotes the values of time domain. In some languages like: Atp[NS94] time domain must be discrete, i.e. isomorphic to the natural numbers. In Lotos NT (as introduced by its predecessors ET Lotos or RT Lotos) the time domain may be dense 3 , i.e. isomorphic to the rational numbers or real numbers. The unique assumption made for time domain is that it is ....

Xavier Nicollin and Joseph Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Information and Computation, 114(1):131--178, 1994.

.... proposed which are intended to model time in a quantitative way: first, synchronous process algebras such as SCCS [Mil 83] Meije [AuB 85] or CIRCAL [Mil 85] and, in a second step, timed process algebras such as TPL (Temporal Process Language) HeR 90] ATP (Algebra of Timed Processes) NRS 90, NS 90, NSY 91] PADS (Process Algebra for Distributed Systems) Azc 90] An overview and synthesis on Timed Process Algebras may be found in [NS 91] In this paper, we present a timed extension of LOTOS, denoted TLOTOS, with the objective of upward compatibility with standard LOTOS. This means that ....

....its use by those who were trained on standard LOTOS. These are our requirements for claiming (true) upward compatibility. They will be further developed in section 2. An upward compatible timed extension to LOTOS 218 TLOTOS has been inspired by other approaches such as TPL [HeR 90] ATP [NS 90] ACP t te [Gro 90] and PADS [Azc 90] Our model is between a strictly asynchronous algebra (like LOTOS, CCS, CSP, ACP) and a strictly synchronous one (like SCCS, CIRCAL, Meije) The idea has been suggested in the works previously mentioned here above and may be informally presented as the ....

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X. Nicollin, J. Sifakis, The Algebra of Timed Processes ATP: Theory and Application, Rept. No. RT-C26, Projet Spectre, LGI-IMAG, Dec. 1990.

....Timed FDTs 339 problem has already led to the creation of many timed FDTs, most of which being either new timed process algebra or quantitative time extensions of well known asynchronous process algebra. For example: ACP r [BaB 90] ACP t te [Gro 90] ATP (Algebra of Timed Processes) NRS 90, NiS 91, NSY 91] 1 , CIRCAL [Mil 85] Estelle [ISO 9074] LOTOS T [MFV 92] Meije [AuB 84] PADS (Process Algebra for Distributed Systems) Azc 90] SCCS [Mil 83] SDL [CCITT Z100] TCCS [MoT 90] TIC [QAF 90] TiCCS (Timed CCS) Wan 90, Wan 91] TiCSP (Timed CSP) ReR 88, Ree 90] Timed arc PN [Wal ....

X. Nicollin, J. Sifakis, The Algebra of Timed Processes ATP: Theory and Application, Rept. No. RT-C26, Projet Spectre, LGI-IMAG, Nov. 1991.

....BoB 87] have been extended and new process algebras have been proposed which are intended to model time in a quantitative way. A non exhaustive list of them are referred to by the following acronyms in the sequel: ACP r [BaB 90] ACP t te [Gro 90a] ATP (Algebra of Timed Processes) NRS 90, NiS 91b, NSY 91] LOTOST [MFV 92] PADS (Process Algebra for Distributed Systems) Azc 90] TCCS (Temporal CCS) MoT 90] TIC [QAF 89] Timed CCS [Wan 90, Wan 91] Timed CSP [ReR 88, DaS 89, Ree 90] Timed interaction LOTOS [BLT 90] TLOTOS [Led 92] T LOTOS and ULOTOS [BoL 92] TPCCS (Timed ....

X. Nicollin, J. Sifakis, The Algebra of Timed Processes ATP: Theory and Application, Rept. No. RT-C26, Projet Spectre, LGI-IMAG, Nov. 1991.

....relations is possible, but this trick does not contribute to comprehensibility. In many applications of TSSs, it is in addition necessary to have support for manysortedness or variable binding operators. Many sortedness is found, for example, in process algebras with timing (see e.g. 4] 8] and [25]) Examples of variable binding operators are the integration operator R of real time ACP [4] and the recursion operator of CSP [21] and CCS [23] Using transition rules to cope with manysortedness is unpractical and obscures the fact that it is a static matter. Variable binding operators can ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

....as troublesome, the modular combination of it with other features has hardly been studied. In this paper, we remedy this situation for discrete time process algebra with relative timing. As far as related work is concerned: most other discrete time process algebras, such as TCCS [17, 20] ATP [21], have only action prefixing, not general sequential composition, and only one mode of termination. Thus, successful and unsuccessful termination cannot be distinguished. Timed CSP does have general sequential composition and two modes of termination: it has the process SKIP for successful ....

....delay operator, notation #(x) also notated # rel (x) see Remark 2.1.3 on page 8) that allows a process to move on to the next time slice. So, the process #(a) when initialized in time slice 5, will execute an a in time slice 6. An important concept we use is the concept of time factorization [21], which enforces that moving into the next time slice does not determine a choice (unless it has to) So, when we initialize the process #(a) #(b) in the first time slice, the choice between a and b is still open after the process has moved into the second time slice, as both #(a) and #(b) can ....

X. NICOLLIN AND J. SIFAKIS. The algebra of timed processes ATP: Theory and application. Information and Computation, 114(1):131--178, 1994.

....the time slices in which they are performed within a time slice there is only the order in which actions are performed. Additionally, performance of actions and passage to the next time slice are separated here. This corresponds to the two phase functioning scheme for modeling timed processes [23]. Note that it means that processes are supposed to be capable of performing certain actions, like in time free process algebra, as well as passing to the next time slice. First we treat the basic discrete relative time process algebra BPA Gamma drt ID. Then we treat PA Gamma drt ID, the ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....to the time slices in which they are performed within a time slice there is only the order in which actions are performed. Additionally, performance of actions and passage to the next time slice are separated here. This corresponds to the two phase functioning scheme for modeling timed processes [25]. Note that it means that processes are supposed to be capable of performing certain actions, like in time free process algebra, as well as passing to the next time slice. A coherent collection of versions of ACP with timing where performance of actions and passage of time are separated, is ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

....with these characteristics was our main motivation to develop it. Different from the real time versions of [2] and [4] this version does not exclude the possibility of two or more actions to be performed consecutively at the same point in time. That is, it includes urgent actions, similar to ATP [37] and the different versions of CCS with timing [19, 35, 44] This is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. This is, for example, the case for actions that happen at different locations in a distributed system. In [2] and [4] ....

....of programming and specification languages, see e.g. 12] 14] and [17] We did not give explicit consideration to other algebraic concurrency theories that deal with time dependent behaviour. In general, they have urgent actions and relative timing. This is, for example, the case with ATP [37], the different versions of CCS with timing [19, 35, 44] and TIC [39] TIC is rooted in LOTOS [46] We claim, on the basis of the connections described in [6] that there are indeed close connections between these theories and the versions of ACP with relative timing presented in this chapter, ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....with these characteristics was our main motivation to develop it. Di erent from the real time versions of [2] and [4] this version does not exclude the possibility of two or more actions to be performed consecutively at the same point in time. That is, it includes urgent actions, similar to ATP [37] and the di erent versions of CCS with timing [19, 35, 44] This is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. This is, for example, the case for actions that happen at di erent locations in a distributed system. In [2] and [4] ....

....of programming and speci cation languages, see e.g. 12] 14] and [17] We did not give explicit consideration to other algebraic concurrency theories that deal with time dependent behaviour. In general, they have urgent actions and relative timing. This is, for example, the case with ATP [37], the di erent versions of CCS with timing [19, 35, 44] and TIC [39] TIC is rooted in LOTOS [46] We claim, on the basis of the connections described in [6] that there are indeed close connections between these theories and the versions of ACP with relative timing presented in this chapter, ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

....Timed frames [7] cover virtually all kinds of transition systems for the discrete time case. Timed frames are in essence the two phase transition systems considered in [6] as the objects underlying discrete time process algebras. They underlie well known discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5] Two phase transition systems are closely related to the real time transition systems that underlie the real time extension of ACP presented in [3] In [4] it is shown that the model of the discrete time extension of ACP based on two phase ....

....scale. It means that the discrete time points just divide real time into time slices and, although actions and state changes take place in real time, only the time slices in which actions and state changes take place are considered to be of importance. Discrete time process algebras such as ATP [26] and the discrete time extension of ACP presented in [5] offer exactly this abstraction. Naturally, it is in accordance with the intended meaning of a time step the passage of time to the next time slice for it derives this meaning from its use in these discrete time process algebras. ....

Nicollin, X. and Sifakis, J.: "The algebra of timed processes ATP: Theory and application", Information and Computation, 114, 1994, 131--178.

....with these characteristics was our main motivation to develop it. Di erent from the real time versions of [1] and [3] this version does not exclude the possibility of two or more actions to be performed consecutively at the same point in time. That is, it includes urgent actions, similar to ATP [30] and the di erent versions of CCS with timing [16, 28, 35] This is useful in practice when describing and analyzing systems in which actions occur that are entirely independent. This is, for example, the case for actions that happen at di erent locations in a distributed system. In [1] and [3] ....

....of programming and speci cation languages, see e.g. 10] 12] and [14] We did not give explicit consideration to other algebraic concurrency theories that deal with time dependent behaviour. In general, they have urgent actions and relative timing. This is, for example, the case with ATP [30], the di erent versions of CCS with timing [16, 28, 35] and TIC [32] TIC is rooted in LOTOS [37] We claim, on the basis of the connections described in [5] that there are indeed close connections between these theories and the versions of ACP with relative timing presented in this paper, i.e. ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

....time stamping of actions can be obtained. The real time versions of ACP presented in [6] unlike those presented in [2] and [3] do not exclude the possibility of two or more actions to be performed consecutively at the same point in time. That is, they include urgent actions, similar to ATP [19] and the di erent versions of CCS with timing [11, 18, 21] This feature seems to be essential to obtain simple and natural embeddings of discrete time versions as well as useful in practice when describing and analyzing systems in which actions occur that are entirely independent. This is, for ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131-178, 1994.

.... 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. Baeten and Bergstra (1991,1992) Davies and Schneider (1995) Hennessy and Regan (1990,1995) Moller and Tofts (1990) Nicollin and Sifakis (1994), Reed and Roscoe (1987) and Yi (1991) 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 ....

Nicollin, X., and Sifakis, J. (1994), The Algebra of Timed Processes ATP: Theory and Application, Information and Computation 114(1), 131--178.

....different approaches for expressing and analyzing time properties of systems have been developed which are based on formal description languages. A first approach concentrates on the aspect of real time, i.e. the expression of time constraints and the verification of exact time properties (see [1, 12] and the references therein) Via this approach the parts of the system that are critical from the viewpoint of time bounds can be validated during the design phase through techniques as e.g. model checking [1] In this view the real time process algebras have been developed by extending the ....

.... bounds can be validated during the design phase through techniques as e.g. model checking [1] In this view the real time process algebras have been developed by extending the standard process algebras with the representation of time and, typically, by introducing some time out operator (see e.g. [12]) A second approach is devoted to the evaluation of the performance of concurrent systems (see [5] and the references therein) According to this approach the time spent by a system in a certain activity is expressed probabilistically through a distribution of duration. Performance measures of ....

X. Nicollin, J. Sifakis, "The Algebra of Timed Processes, ATP: Theory and Application", in Information and Computation 114:131-178, 1994

....perform an action. Even worse, trying to identify these moments only obscures the interpretation of timing constraints. It appears that this alternative interpretation of timing constraints has been originated from some work on the introduction of timing in process algebras, such as [2] 3] 4] [5], 6] 7] and [10] to name just a few. In most of these models, timing is defined in terms of the time span between actions, periods when behaviours are wishing to participate in actions, and time passage itself, which means that the time concept becomes actually implemented in the process ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Technical Report RT-C26, LGI-IMAG, Grenoble, France, Dec. 1990.

....congruence in the presence of priority have been restricted to finite, i.e. recursion free processes [34] In that approach priority is nicely reflected by the following axiom, where a has a lower priority than b: P a:Q = P . A variety of timed process algebras has also been proposed [40, 21, 32, 4, 43, 36, 2, 12]. A thorough overview of the basic ingredients is given in [35] Complete proof systems for regular expressions have been obtained for some of these calculi [23, 1, 15] One of the typical features of CCS based timed process algebras is a notion of maximal progress, also called minimal delay or ....

X. Nicollin and J. Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Information and Computation 114:131-178, 1991.

.... for , etc. are currently missing and should be added if possible; 3. Regarding real time aspects, ECSs must be kept simple in order to meet certification requirements. It is therefore likely that the real time aspects can easily be expressed using timed process algebras such as ATP [NS91, NS94] or timed versions of Lotos [BL91, LL92, QFA93] Although the objectives of the FLAIR study were probably too ambitious for the current state of the art in formal methods, the authors still believe that the FLAIR principles are sound: formal methods, verification techniques, and automatic code ....

Xavier Nicollin and Joseph Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Information and Computation, 1994. To appear.

....of tasks that compete for shared resources. Most current real time formalisms adequately capture delays due to component synchronization, e.g. Statecharts [10] Modechart [18] Communicating Real time State Machine [32] and timed extensions of the classic untimed process algebras CSP and CCS [8, 15, 25, 35, 27]. These formalisms, however, abstract out resource specific details. This motivated the Communicating Shared Resources (CSR) paradigm [19, 21] to provide a formalism where the run time resource requirements of a real time system can be specified together with its functional and temporal ....

X. Nicollin and J. Sifakis. The Algebra of Timed Processes ATP: Theory and Application. Technical Report RT-C26, Institut National Polytechnique De Grenoble, November 1991.

....steps representing the execution of actions and the passage of time to the next time slice, respectively. Equipped with a root marker and optionally with termination markers, timed frames make up the transition systems that match with the twophase functioning scheme for modeling timed processes [10]. There is a well developed tradition of thinking about transition systems from modal logic (for an overview of modal formalisms for describing transition systems, see e.g. 11] Process algebra studies transition systems at a more abstract level: transition systems modulo an appropriate process ....

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: Theory and application. Information and Computation, 114:131--178, 1994.

....the average temperature is computed within 5sec. Furthermore, some languages also include constructs describing implementation dependent primitives, such as priorities and execution speeds of CPUs. Most of the design languages employ a process algebra formalism e.g. wTCCS[38] Timed CSP[35] ATP[33], Esterel[8] Signal [7] few are based on a data flow paradigm e.g Lustre, TB nets[18] In general, such languages are executable, and some are supported by visual representation (Statecharts [24] As most RTS are large scale, it is desired that specification languages support gradual ....

....variable (the interpretation of time is given by the user) Thus in order to reason about real time progress one needs a special set of equations defining its nature. ATP There are a number of process algebra languages intended for RTS specifications. The most suitable seems to be ATP [33] which augments CSP with special time variables and the activation constructs: Timeout and Watchdog (other extensions of CSP [35] rely on a special delay construct for the specification of time progress) ATP employes a (dense) time domain to represent an execution of a process. In the language ....

X. Nicolin and J. Sifakis. The algebra of timed processes atp: Theory and application. Technical Report RT-C26, LGI-IMAG, France, 1990.

....greater than the longest duration of a step computed so as to take into account execution time of sequences of ideally zero time actions. The assumption about eventual progress of time guarantees that such a bound exists. Following these ideas, the Algebra of Timed Processes ATP has been studied [NRSV90, NS90]. In these papers we considered that the time domain is discrete and this was implemented by assuming that processes can perform, apart from ordinary actions, a special time action represented by , whose synchronous execution makes time progress by one unit. Apart from standard operators of ....

....and illustrated by two examples. A definition is proposed, yielding a quite simple operational semantics. 2 ATPD : ATP for a time domain D We present here a generic version of the algebra ATP, parametrized with an arbitrary time domain. For a complete theory of ATP, the reader should refer to [NS90]. The primitive constructs of ATP in this paper are different from those presented in [NS90] We introduce the notion of delayable action, and the start delay operator of [NS90] is replaced by a timeout operator. These modifications are motivated by the fact that the timeout operator is much ....

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X. Nicollin and J. Sifakis. The algebra of timed processes ATP: theory and application. Information and Computation, (to appear), December 1990.

....q 0 letting time progress by d time units. This model is used to define the operational semantics of the specification language. 3 A real time specification language In this section we define the syntax and semantics of our specification language which is a version of the process algebra ATP [NRSV90, NS90, NSY91, Nic92]. ATP is extensively studied in [NS90] and more recently in [Nic92] where a complete and sound axiomatization is provided. ATP is compared with other real time process algebras in [NS91] 3.1 Syntax and semantics Let P roc be a set of names for processes. The syntax of the language is defined ....

....used to define the operational semantics of the specification language. 3 A real time specification language In this section we define the syntax and semantics of our specification language which is a version of the process algebra ATP [NRSV90, NS90, NSY91, Nic92] ATP is extensively studied in [NS90] and more recently in [Nic92] where a complete and sound axiomatization is provided. ATP is compared with other real time process algebras in [NS91] 3.1 Syntax and semantics Let P roc be a set of names for processes. The syntax of the language is defined by the following grammar: S : spec Y ....

[Article contains additional citation context not shown here]

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: theory and application. Technical Report RT-C26, LGI-IMAG, France, December 1990. To appear in Information and Computation.

....greater than the longest duration of a step computed so as to take into account execution time of sequences of ideally zero time actions. The assumption about eventual progress of time guarantees that such a bound exists. Following these ideas, the Algebra of Timed Processes ATP has been studied [NRSV90, NS90]. In these papers we considered that the time domain is discrete and this was implemented by assuming that processes can perform, apart from ordinary actions, a special time action represented by , whose synchronous execution makes time progress by one unit. Apart from standard operators of ....

....is proposed, yielding a quite simple operational semantics. Acta Informatica 30, 181 202 (1993) 4 2 ATPD : ATP for a time domain D We present here a generic version of the algebra ATP, parametrized with an arbitrary time domain. For a complete theory of ATP, the reader should refer to [NS90]. The primitive constructs of ATP in this paper are different from those presented in [NS90] We introduce the notion of delayable action, and the start delay operator of [NS90] is replaced by a timeout operator. These modifications are motivated by the fact that the timeout operator is much ....

[Article contains additional citation context not shown here]

X. Nicollin and J. Sifakis. The algebra of timed processes ATP: theory and application. Information and Computation, (to appear), December 1990.

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Nicollin, X., Sifakis, J.: The algebra of timed processes ATP: theory and application, Information and Computation, Vol. 114(1), pp. 131-178, (1994).

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X. Nicollin, J. Sifakis, The algebra of timed processes ATP: Theory and application, Information and Computation 114 (1994) 131--178.

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X. Nicollin and J. Sifakis. The algebra of timed processes ATP: theory and application. Information and Computation, 114(1):131--178, Oct. 1994.

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