F. Moller and C. Tofts. Relating processes with respect to speed. In J. Baeten and J. Groote, editors, CONCUR '91, Lect. Notes Comp. Sci. 527, 424-438. Springer, 1991.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....a corresponding bisimulation based faster than relation was studied in [LV01] Upper time bounds have also been studied in the area of distributed algorithms, see e.e. Lyn96] A bisimulation based faster than relation for asynchronous systems using lower time bounds has been suggested in [MT91]. Since this paper develops our previous approach further, we refer the reader to [CVJ00] for a comparison of this approach with the literature, in particular on other timed process algebras. Continuing [JV99, CVJ00] we have shown in this paper that the qualitative faster than relation can also ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J. Baeten and J. Groote, editors, CONCUR '91, Lect. Notes Comp. Sci. 527, 424-438. Springer, 1991.

....in [19] yield formulae whose size is linear with respect to that of the timed automaton they characterize. We present characteristic formula constructions for timed bisimilarity [28] timed versions of the simulation [21] and ready simulation [5, 20] preorders and for the faster than preorder [23]. In particular, the characteristic formula construction for timed bisimilarity improves upon that o#ered in [19] In addition, since, if B is a deterministic timed automaton, checking whether the set of timed traces a#orded by a timed automaton A is included in that of B is equivalent to ....

....and detailed references to the original literature) and some of them (e.g. bisimulation and trace equivalence) have later been adapted to a timed setting. However, the timed setting also provides specific time dependent behavioral relations. One such relation is the faster than bisimulation from [23], which explicitly requires one process to execute at least as fast as another, while having the same functional behaviour. See [3] for a similar proposal in the more classic setting of CCS [22] We now proceed to review the timed behavioural relations over TLTSs studied in this paper. The ....

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F. Moller and C. Tofts, Relating processes with respect to speed, in CONCUR '91: 2 International Conference on Concurrency Theory, J. C. M. Baeten and J. F. Groote, eds., vol. 527 of Lecture Notes in Computer Science, Amsterdam, The Netherlands, 26--29 Aug. 1991, Springer-Verlag, pp. 424--438.

....systems. An elegant proof of decidability of bisimilarity for BPP was given in [8] while all other equivalences in van Glabbeek s spectrum are undecidable in BPP [15, 17] In order to deal with timing aspects of systems, process algebras were extended with an appropriate notion of time (see e.g. [20], 1] 14] 10] 9] 2] A substantial effort have also been directed toward defining a robust notion of equivalence taking performance into consideration, e.g. equivalence that relates only those processes that exhibit the same behavior at the same speed. The bisimilarity investigated in ....

F. Moller and C. Tofts. Relating processes with respect to speed. In Proc. 2nd Int Conf. Concurrency Theory (CONCUR'91), LNCS 527, pages 424--438, 1991.

....Timed Interaction LOTOS and Timed Petri Nets. Untimed bisimulation equivalence is introduced in order to consider the two pro cesses, which behave the same but in different time constraints (e.g. in different speed) be equivalent. Similar but more advanced investigations are made for CCS in [21, 22]. 16 ....

F. Moller and C. Tofts, "Relating processes with respect to speed," in Proc. of CONCUR '91, vol. 527 of Lecture Notes in Computer Science, pp. 424-438, Springer-Verlag, 1991.

.... [LLW95] this problem has been shown decidable using the region technique of Alur and Dill [AD94, ACD90] The region technique provides an abstract interpretation of timed automata sufficiently complete that all information necessary for model checking It may be shown that the speed relation of [FT91] is characterized in a similar manner by Y defined recursively by Y V a2A ( a1 ]99ha2 iY [a2 ]ha1iY ) 88Y . with respect to L is maintained, yet finitary and thus enabling standard algorithmic model checking techniques to be applied. The basic idea is that, given a timed automaton A, ....

F.Moller and C. Tofts. Relating Processes with Respect to Speed. Technical Report ECS--LFCS--91--143, Department of Computer Science, University of Edinburgh, 1991.

....systems. Currently available languages are: Design language Command line argument Milner s Calculus of Communicating Systems (CCS) 20] ccs Milner s Synchronous Calculus of Communicating Systems (SCCS) 19] sccs Version of CCS with prioritized actions [8] pccs Version of CCS with timed actions [21] tccs Hoare s Communicating Sequential Processes (CSP) 17] csp Basic Lotos [3] lotos The examples here use CCS as the design language. The tool is used in exactly the same fashion for other languages. See Section 7 for details on the syntax and semantics of each language. If the gui ag is ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J.C.M. Baeten and J.F. Groote, editors, CONCUR '91, volume 527 of Lecture Notes in Computer Science, pages 424-438, Amsterdam, August 1991. Springer-Verlag.

....would allow models to be manipulated whilst retaining knowledge that the new model, while not necessary maintaining an exact representation, satisfies certain relations with respect to the original model. This could perhaps be similar to the faster than relation developed for a subset of TCCS in [50]. An alternative compositional approach to the solution of Markov processes is the use of tensor algebra to express the generator matrix of a process. This approach has been proposed by Plateau et al. . for Stochastic Automata Networks [51] Donatelli for Superposed Stochastic Automata and ....

F. Moller and C. Tofts. Relating Processes with Respect to Speed. Technical Report ECS-LFCS91 -143, LFCS, Department of Computer Science, University of Edinburgh, March 1991.

....automaton model of [40] where both pure and probabilistic nondeterminisms are present. Multiple success actions are used rather than a single success action in order to observe the relative probabilities of different traces within a computation. 2. 3 Timed Nonprobabilistic Processes In [33] an efficiency relation is studied for TCCS [32] a timed extension of CCS where a deterministic time prefix operator is included. This relation is formalized by means of a bisimulation preorder which relates two functionally equivalent processes whenever one of them performs more quickly than the ....

F. Moller, C.M.N. Tofts, "Relating Processes with Respect to Speed", in Proc. of the 2nd Int. Conf. on Concurrency Theory (CONCUR '91), LNCS 527:424-438, Amsterdam (The Netherlands), 1991

....This section presents two algebraic order relations on distributed real time objects with respect to speed. In the last few years, many timed equivalence relations for synchronously communicating processes (or objects) have already been explored in timed extended process calculi (for example see [13, 14, 16]) These relations equate two processes only when their temporal and behavioral properties completely match. The temporal strictness of these relations is appropriate in verifying synchronously communicating real time objects. This is because every sender object must synchronize its receiver one ....

....foundation for asynchronous communication with port passing mechanism, 15 and it does not provide any support for the notion of time. There have been many timed extensions of process calculi for synchronous communication, for example [8, 14, 16] There is a notable work by Moller and Tofts in [13] where the authors studied a preorder relation over timed processes with respect to speed based on the bisimulation concept, like ours. However, their order relation is seriously dependent on synchronous communication and thus cannot deal with asynchronous interactions among distributed objects. ....

Moller, F., and Tofts, C., Relating Processes with Respect to Speed, Proceedings of CONCUR'91, LNCS 527, p424-438, August, 1991.

....of Bologna Piazza Porta S. Donato 5, 40127 Bologna, Italy. 1 1 Introduction 1 Introduction Recently, in the field of semantics for process description languages, a great deal of interest has been stirred up by equivalence notions which incorporate some measure of efficiency (see, e.g. [18, 4, 2, 12]) Some of them [2, 3, 10, 12] rely on the basic idea that processes are discriminated not only according to their functionality (what actions the processes can do) but also considering their performance (a measure of the time consumed for their execution) Particularly relevant for the present ....

....that communications are often the most expensive operations to be performed in a distributed system. However, no performance measure is available for a language without internal actions; furthermore, it maybe debatable to count time passing by counting the execution of (unobservable) actions. In [18] a faster than relation has been studied for a language in the so called abstract time approach: actions are atomic and time passes in between them via explicit global synchronizations. The observer is, unlike us, interacting with the system, imposing through the interaction the ....

F.Moller, C.Tofts, Relating Processes with Respect to Speed. In CONCUR'91,LNCS 527, SpringerVerlag, pp. 424-438, 1991.

....is a negative side in TPA and Timed CCS. Once an action is enabled, it is not disabled directly. Therefore, these calculi are di#cult to express some indispensable temporal facilities found in distributed systems such as timeout handling. Timed Extension: Timed Restriction. Moller and Tofts in [53, 54, 75] develop a time extension of CCS. It is characterized by the following primitives: 0, #.P , t) P , and P # P . 0 corresponds to a terminate process but does not allow time to pass; #.P corresponds to the derived arbitrary delay operator of in SCCS [50] and is willing to wait any amount of time; ....

....relations such as bisimulation equivalence [58] trace equivalence [11] failure equivalence [11] and testing equivalence [21] but they cannot distinguish between the timings of processes. Several researchers have explored time extensions of the strong bisimulation [51] for example see [27, 14, 17, 26, 54, 57, 64, 75, 79]. The extended bisimulations equate two processes if they cannot be distinguished from each other in their temporal properties as well as their behavioral one. Most of them are di#cult to have the concept of observation, because their timed semantics often disable internal actions to be ignored ....

[Article contains additional citation context not shown here]

F. Moller and C. Tofts. Relating Processes with Respect to Speed. In Proceeding, 2th CONCUR'91, volume 527 of Lecture Notes in Computer Science, pages 424-- 438. Springer-Verlag, 1991.

....for example [3, 20, 28] Most of the calculi have been equipped with time sensitive equivalence relations which equate two processes only when they are behaviorally and temporally equivalent. But only a few of them provide a method to compare temporal costs of parallel systems, for example [7, 15, 23]. Moller and Tofts in [15] and Jenner and Vogler in [7] proposed preorder relations over parallel processes with respect to their relative speeds. However, unlike ours, the semantics of the relations assumes to permit an executable communication to be suspended for arbitrary periods of time, and ....

....Most of the calculi have been equipped with time sensitive equivalence relations which equate two processes only when they are behaviorally and temporally equivalent. But only a few of them provide a method to compare temporal costs of parallel systems, for example [7, 15, 23] Moller and Tofts in [15] and Jenner and Vogler in [7] proposed preorder relations over parallel processes with respect to their relative speeds. However, unlike ours, the semantics of the relations assumes to permit an executable communication to be suspended for arbitrary periods of time, and thus cannot exactly predict ....

Moller, F. and Tofts, C., Relating Processes with Respect to Speed, Proceedings of CONCUR'91, LNCS, Vol.527, Springer-Verlag, 1991.

....between TPL [26] and ACP drt , only TPL is based on testing equivalence instead of bisimulation equivalence. Timed CSP [21] which is based on timed traces and timed failures, has urgent actions and relative timing as well. In [20] the CCS like process algebras with timing of [26] 35] [36] and [44] are compared. For comprehensive overviews of existing algebraic concurrency theories that deal with time dependent behaviour, having their roots in ACP, CCS, CSP, LOTOS or others, the reader is referred to Chapter 12 of [30] and Chapter 8 of [42] These overviews include discussions of ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J.C.M. Baeten and J.F. Groote, editors, CONCUR'91, pages 424--438. LNCS 527, Springer-Verlag, 1991.

....probability, locality, etc. In the timed framework, some efforts have been directed toward defining a robust notion of performance , that would allow comparing the efficiency of systems that have the same functional behaviour (what they do) but different speeds (how fast they do it) See, e.g. [MT91,AH92,FM95,GRS95,CGR97,Cor98]. Durational urgent actions. The efficiency preorders and equivalences considered in [GRS95,AM96,CGR97,Cor98] apply to process algebras where parallel components have their own independent local clocks, where actions have a duration and are urgent. Urgent actions take place as soon as possible ....

F. Moller and C. Tofts. Relating processes with respect to speed. In Proc. 2nd Int. Conf. Theory of Concurrency (CONCUR'91), Amsterdam, NL, Aug. 1991, volume 527 of Lecture Notes in Computer Science, pages 424--438. Springer, 1991.

....between TPL [26] and ACP drt , only TPL is based on testing equivalence instead of bisimulation equivalence. Timed CSP [21] which is based on timed traces and timed failures, has urgent actions and relative timing as well. In [20] the CCS like process algebras with timing of [26] 35] [36] and [44] are compared. For comprehensive overviews of existing algebraic concurrency theories that deal with time dependent behaviour, having their roots in ACP, CCS, CSP, LOTOS or others, the reader is referred to Chapter 12 of [30] and Chapter 8 of [42] These overviews include discussions of ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J.C.M. Baeten and J.F. Groote, editors, CONCUR'91, pages 424-438. LNCS 527, Springer-Verlag, 1991. 45

....between TPL [21] and ACP drt , only TPL is based on testing equivalence instead of bisimulation equivalence. Timed CSP [18] which is based on timed traces and timed failures, has urgent actions and relative timing as well. In [17] the CCS like process algebras with timing of [21] 28] [29] and [35] are compared. ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J.C.M. Baeten and J.F. Groote, editors, CONCUR'91, pages 424-438. LNCS 527, Springer-Verlag, 1991.

.... problem, which when combined with the model checking algorithm for L yields an alternative algorithm for timed bisimulation compared with [Cer92] In addition, characteristic formula constructions may be given for time abstracted equivalence [LW93] and the faster than relation in [FT91], immediately yielding 2 or a kripke structure 3 decision procedures for these relationships as well; Second, we prove decidability of bounded satisfiable for L . That is, we present a model construction algorithm, which given a formula of L and bounds k and M will synthesize a timed ....

....in a number of directions: The notion of a characteristic formula construction may be applied to other behavioural preorders in order to obtain corresponding preorder checking algorithms. We have already shown that characteristic formula constructs also exists for the faster than relation in [FT91] and the time abstracted equivalence in [LW93] The results of this paper only solve (positively) the decidability of a bounded satisfiability problem for L . However, it follows from this result that the unconstrainted satisfiability problem is at least r.e. though we conjecture that this ....

F.Moller and C. Tofts. Relating Processes with Respect to Speed. Technical Report ECS--LFCS--91--143, Department of Computer Science, University of Edinburgh, 1991.

....of continuous algebra. Though CCS allows the analysis of the temporal ordering of events, there is no way to specify the relative speeds of events. Synchronous CCS (SCCS) has been studied by Milner [Mil83] in which events are synchronized by timesteps. Timed CCS (TCCS) has also been proposed [MT90, MT91] as a tool for real time analysis, which introduces willing to delay and forcing to delay operators. Many basic tools for communication protocol specification and verification are CCS like languages [QAF89, Atl89] Some more general work on the semantics of communicating processes has been ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J.C.M. Baeten and J.F. Groote, editors, CONCUR-91, number 527 in Lecture Notes on Computer Science. Springer-Verlag, 1991. BIBLIOGRAPHY 188

....between events (e.g. 6] location information (e.g. 4] port passing mechanism (e.g. 8, 11] and local time (e.g. 17] but none addresses the issue of communication delay. Also, there have been several temporal extensions of process calculi for synchronous communication, for example [7, 13, 14, 16, 20, 22]. Among these, Moller and Tofts in [13] studied a preorder relating timed processes with respect to speed. However, the order relation is inherently dependent on synchronous communication and thus cannot compare the performances of asynchronously communicating processes. On the other hand, there ....

....[4] port passing mechanism (e.g. 8, 11] and local time (e.g. 17] but none addresses the issue of communication delay. Also, there have been several temporal extensions of process calculi for synchronous communication, for example [7, 13, 14, 16, 20, 22] Among these, Moller and Tofts in [13] studied a preorder relating timed processes with respect to speed. However, the order relation is inherently dependent on synchronous communication and thus cannot compare the performances of asynchronously communicating processes. On the other hand, there are many process calculi with the ....

Moller, F., and Tofts, C., Relating Processes with Respect to Speed, Proceedings of CONCUR'91, LNCS 527, Springer-Verlag, August, 1991.

....distinguishes some systems which are equivalent here. The approach of [AKH92] was recently varied in [AKN95] while [AKH92] compares the worst case as well as the best case, the new variant only takes the worst case into account (as we have done here) Faster than relations are also presented in [HR90, CZ91, MT91, CGR95]. In the first two papers, the behaviour of systems is influenced by timing considerations, i.e. the systems are not asynchronous. In [MT91] also a bisimulation type preorder is defined and actions are regarded as instantaneous; a unit time delay operator with a special treatment is introduced, ....

....the best case, the new variant only takes the worst case into account (as we have done here) Faster than relations are also presented in [HR90, CZ91, MT91, CGR95] In the first two papers, the behaviour of systems is influenced by timing considerations, i.e. the systems are not asynchronous. In [MT91], also a bisimulation type preorder is defined and actions are regarded as instantaneous; a unit time delay operator with a special treatment is introduced, which makes the comparison to our approach very difficult. Such an operator is also used in [HR90] where a testing scenario is developed ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J. Baeten and J. Groote, editors, CONCUR '91, Lect. Notes Comp. Sci. 527, 424--438. Springer, 1991.

....is a negative side in TPA and Timed CCS. Once an action is enabled, it is not disabled directly. Therefore, these calculi are difficult to express some indispensable temporal facilities found in distributed systems such as timeout handling. Timed Extension: Timed Restriction. Moller and Tofts in [53, 54, 75] develop a time extension of CCS. It is characterized by the following primitives: 0, ffi:P , t) P , and P 8 P . 0 corresponds to a terminate process but does not allow time to pass; ffi:P corresponds to the derived arbitrary delay operator of in SCCS [50] and is willing to wait any amount of ....

....relations such as bisimulation equivalence [58] trace equivalence [11] failure equivalence [11] and testing equivalence [21] but they cannot distinguish between the timings of processes. Several researchers have explored time extensions of the strong bisimulation [51] for example see [27, 14, 17, 26, 54, 57, 64, 75, 79]. The extended bisimulations equate two processes if they cannot be distinguished from each other in their temporal properties as well as their behavioral one. Most of them are difficult to have the concept of observation, because their timed semantics often disable internal actions to be ignored ....

[Article contains additional citation context not shown here]

F. Moller and C. Tofts. Relating Processes with Respect to Speed. In Proceeding, 2th CONCUR'91, volume 527 of Lecture Notes in Computer Science, pages 424-- 438. Springer-Verlag, 1991.

....one can say that we assume safety (the instantaneous accesses do not overlap) but require liveness in a limited way only: an access can be blocked by repeated writes but not by repeated reads modelled by read arcs. We close by shortly listing some faster than relations from the literature. [AKH92, MT91, CGR95] define bisimulation type preorders and require functional equivalence, i.e. the faster implementation has to perform the same actions as the specification, hence these approaches are sometimes more discriminating than ours. HR95, CZ91, NC96] are testing based, but only the third uses some bound ....

....functional equivalence, i.e. the faster implementation has to perform the same actions as the specification, hence these approaches are sometimes more discriminating than ours. HR95, CZ91, NC96] are testing based, but only the third uses some bound in the tests (similar to our test duration) In [HR95, MT91], a unit time delay operator with a special treatment is introduced, while actions take no time; hence, the parallel execution of two actions is equated with their arbitrary interleaving, but these are different in the present paper since actions may take up to time 1. Our approach similarly ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J. Baeten and J. Groote, editors, CONCUR '91, Lect. Notes Comp. Sci. 527, 424--438. Springer, 1991.

....r ]ha l iZ j 88Z Then timed bisimilarity between timed transition systems is characterized as follows 10 : Theorem 4. Let S be a timed transition system over A, and let s 1 , s 2 be states of S. Then s 1 s 2 if and only if s 1 j h s 2 j= E Z . 10 It may be shown that the speed relation of [20] is characterized in a similar manner by Y defined recursively by Y def = V a2A ( a1 ]99ha2 iY [a2 ]ha1iY ) 88Y . 4 Regions The model checking problem for L consists in deciding if a given timed automata A satisfies a given specification in L . In [16] this problem has been shown ....

F. Moller and C. Tofts. Relating Processes with Respect to Speed. Technical Report ECS--LFCS--91--143, Department of Computer Science, University of Edinburgh, 1991.

....simultaneous execution of actions on the determination of when a system works faster than another are explored in [17] But none of them contain an algebraic theory or full abstractness result as we have developed here. Theories for relating processes on the basis of their speed also appear in [13, 5]. None of them present any kind of full abstractness result. Acknowledgements: We would like to thank S. ArunKumar for several insightful comments. ....

F. Moller and C. Tofts. Relating processes with respect to speed. In J. Baeten and J. Groote, editors, CONCUR '91, volume 527 of Lecture Notes in Computer Science, pages 424--438, Amsterdam, Aug. 1991. Springer-Verlag.

....understudy, and the results obtained have been derived directly from these formal descriptions. Throughout we make use of process algebraic notation [Mil90] to formally describe the systems under consideration. In particular we use notations that permit the description of real time properties [MT90, MT91, MT92, MT93] and probabilistic and priority properties [Tof90, Tof94] 2 Deterministic costs Previous analyses of asynchronous pipelines [Wil90, SS93, Wil94] of the performance of asynchronous pipelines have been holistic approaches to the determination of the circuit performance. In this section we shall ....

....to make use of timed extensions of Milner s [Mil80, Mil90] Calculus of Communicating Systems (CCS) called TCCS [MT90] to describe the behaviour of a micropipeline stage and its environment. 2. 1 Introduction to TCCS For a full description of the timed extension to Milner s CCS[Mil80, Mil90] see [MT90, MT91, MT92, MT93]. CCS is based on the notion of interleaving parallelism and handshake communications, with a being an input action and a an output, with representing a completed communication between an input and output pair. 1 Valid Don t care Valid Acknowledge Data End Start End Start Computation 1 ....

Moller, F. and C. Tofts, Relating Processes with Respect to Speed, Proceedings of CONCUR'91, Lecture Notes in Computer Science 527, (Theories of Concurrency: Unification and Extension), Amsterdam, August 1991.

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