Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI:171-199, 1992.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....pa city ina sta te to execute wea k tra nsitions la belled bya n observa blea ction. Nevertheless, wea k congruence is nota s undisputeda mong the va st number of wea rela tionsa s strong bisimila rity is a ong the strong rela tions. Some, e.g. va n Gla bbeek Weijla d [54]a nd Montaa5 Sa ssone [41] point out tha wea k bisimila rity is too coa rse to preserve the precise bra nching structure of a process. Others, like DaO1 dea [14] Va ma ri [53] de Nicolaz ennessy [44] Pa rrow Sjodin[48] Clea vela nd Na ta rja n[42] a swella sBrinksma et al. 9] defineaS0 n coa61fi equiva encesa da rgue ....

U. Montanari and V. Sassone. Dynamic Congruence vs. Progressing Bisimulation for CCS. Fundamenta Informaticae, XVI(2):171--199, 1992.

....as a candidate for type equivalence. Furthermore, we want :l and : l to be equivalent, because the number of unblockings cannot be counted from within the object as they correspond to transitions on other objects, thus discarding strong bisimulation [Mil89a] and progressing bisimulation [MS92] We also want to distinguish l: m from l:m on the grounds that, for the latter, a blocking after l cannot be observed, and thus observational congruence [Mil89a] and rooted bisimulation [BBK87] are unsuitable. Also, notice that all the above mentioned equivalences, with the exception of weak ....

....be matched by at least one silent action (cf. the observational congruence, oc) Hence, lsc is ner than oc (as lsb is ner than wb) since the laws of lsc are particular cases of the laws of oc. In CCS, the coarsest bisimulation which is still a congruence is the progressing bisimulation (pb) MS92] Notice that lsc is incomparable to pb, as, e.g. l: m 6= pb l: m but l: m lsc l: m, and l :l = pb :l but l :l 6 lsc :l. In ABT, wb is a congruence, as the sums are pre xed. Since this setting has no mixed sums, the laws are particular cases of the laws holding for wb. ....

Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16(2):171-199, 1992.

....q holds) Note that in general is not a bisimulation. The largest congruence Research supported by the IST programme on FET GC Projects AGILE, MYTHS and SOCS. which is also a bisimulation is called dynamic bisimilarity and it is defined by allowing context closure at each bisimulation step [22]. To avoid universal quantification on contexts, several authors e.g. Sewell in [25] Leifer and Milner in [20] propose a symbolic transition system for components whose labels are the minimal contexts needed to the component for evolving. A transition X 1 means that ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171--196, 1992.

....as a candidate for type equivalence. Furthermore, we want #.l and #.#. l to be equivalent, because the number of unblockings cannot be counted from within the object as they correspond to transitions on other objects, thus discarding strong bisimulation [Mil89a] and progressing bisimulation [MS92]. We also want to distinguish l.#.m from l.m on the grounds that, for the latter, a blocking after l cannot be observed, and thus observational congruence [Mil89a] and rooted bisimulation [BBK87] are unsuitable. Also, notice that all the above mentioned equivalences, with the exception of weak ....

....be matched by at least one silent action (cf. the observational congruence, oc) Hence, lsc is finer than oc (as lsb is finer than wb) since the laws of lsc are particular cases of the laws of oc. In CCS, the coarsest bisimulation which is still a congruence is the progressing bisimulation (pb) [MS92]. Notice that lsc is incomparable to pb, as, e.g. l.#.m pb l.#.#.m but l.#.m lsc l.#.#.m, and l #.l = pb #.l but l #.l lsc #.l. In ABT, wb is a congruence, as the sums are prefixed. Since this setting has no mixed sums, the # laws are particular cases of the laws holding for wb. ....

Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16(2):171--199, 1992.

....the correctness of an encoding in Section 5.5. Deviating from the standard presentation of expansion, we introduce some auxiliary terminology that will be useful in the next subsection for capturing aspects of divergence. It is partly inspired by the notion of progressing bisimulation in CCS [MS92b]. Definition 2.3.4 A weak simulation progressing, if P = # Q # such that (P # , Q # ) strict, if P for all (P, Q) and for all being # or output with bn( Note that a weak simulation is strong if it is both progressing and strict. Definition 2.3.5 (Expansion) A binary ....

U. Montanari and V. Sassone. Dynamic Congruence vs. Progressing Bisimulation for CCS. Fundamenta Informaticae, XVI(2):171--199, 1992.

....method l .Wealsowanttodistinguishl.#mfrom l .m, on the grounds that for the latter a blocking after l cannot be observed. This also discards Milner s observational congruence [4] and rooted bisimulation [1] as possible candidates for object equivalence. A notion such as progressing bisimulation [5] is however too strong because it would distinguish ## from ###. These considerations lead to the choice of a notion of equivalence that essentially strengthens weak bisimulation by requiring that if # and # are bisimilar and # o#ers a particular method then also # o#ers that method. Definition ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16 (2):171--199, 1992.

....transitions in the tests of De Nicola and Hennessy [12] The expressive power of their cal4 culi suces to recover early labelled transition bisimulations as the induced congruences. Related work of Honda and Yoshida [24] uses insensitivity as the basic observable; that of Montanari and Sassone [31] takes the usual CCS labelled transitions but by requiring context closure at every step of a bisimulation gives the coarsest notion of weak bisimulation that is simultaneously a congruence. Rensink [40] studies bisimulation directly on open terms. to labelled transitions Summarizing, de ....

Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI:171-199, 1992.

....2 j R Gamma P 2 f b =xg j R 0 . Since is closed under substitution, we have P 0 1 f b =xg P 2 f b =xg, hence P 0 1 f b =xg j R 0 S P 0 2 f b =xg j R 0 . Therefore is both a bisimulation and a congruence. This reminds us of Montanari and Sassone s dynamic bisimulation [MS92]. The latter has been introduced in CCS to study systems which allow for dynamic reconfigurations. When bisimilar, such systems can be consistently substituted one for the other in any context and at any time of their life. We present here the strong version of dynamic bisimulation for the ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI(2):171--199, 1992.

....weak bisimulation as a candidate for type equivalence. However, we want #.l and #.#. l to be equivalent because the number of unblockings cannot be counted from within the object as they correspond to transitions on other objects, which discards strong bisimulation [13] and progressing bisimulation [15]. We also want to distinguish l.#.m from l.m on the grounds that for the latter a blocking after l cannot be observed, and thus observational congruence [13] and rooted bisimulation [1] are unsuitable. Also, notice that in a sense all the above mentioned equivalences, with the exception of weak ....

Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16 (2):171--199, 1992.

....bisimilarity, rather than outside. We see no technical difficulty in adapting our proof techniques to this equivalence, with the exception of the weak version of polymorphic bisimulation, for whose soundness some modifications would be need (technically speaking, we should take the dynamic version [MS92b] of polymorphic bisimulation) The definition of may testing equivalence [DH84, Hen88, BD92] is similar to that of weak barbed equivalence, but the bisimulation game on interactions is removed. In the definition of must testing in addition, the observability predicates P a indicate the ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI(2):171--199, 1992.

....into account by stating that one process engages in at least as many internal actions as another. Thus, its definition pays more attention to internal steps. We introduce some auxiliary terminology that will be useful later on. It is partly inspired by the notion of progressing bisimulation in CCS [MS92b]. Definition 2.3.4 A weak simulation S is called ffl progressing, if P Gamma Gamma P 0 implies that there is Q 0 with Q = Q 0 such that (P 0 ; Q 0 ) 2 S. ffl strict, if P Gamma Gamma P 0 implies that there is Q 0 with Q b Gamma Gamma Q 0 such that (P 0 ; ....

U. Montanari and V. Sassone. Dynamic Congruence vs. Progressing Bisimulation for CCS. Fundamenta Informaticae, XVI(2):171--199, 1992.

....l . We also want to distinguish l : m from l :m, on the grounds that for the latter a blocking after l cannot be observed. This also discards Milner s observational congruence [4] and rooted bisimulation [1] as possible candidates for object equivalence. A notion such as progressing bisimulation [5] is however too strong because it would distinguish ]ff from ] ff. These considerations lead to the choice of a notion of equivalence that essentially strengthens weak bisimulation by requiring that if ff and fi are bisimilar and ff offers a particular method then also fi offers that method. ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16 (2):171--199, 1992.

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U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171-196, 1992.

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U. Montanari, V. Sassone, Dynamic congruence vs. progressing bisimulation for CCS, Fundamenta Informaticae 16 (1992) 171--196.

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U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171--196, 1992.

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U. Montanari, V. Sassone, Dynamic congruence vs. progressing bisimulation for CCS, Fundamenta Informaticae 16 (1992) 171--196.

....the external world should be considered, but also experiments consisting of the additions of new components. In our setting, this corresponds to allow an extra clause in the de nition of bisimulation where arbitrary contexts are applied. The resulting notion of equivalence has been considered in [26] and called dynamic bisimilarity. Of course, when ordinary bisimilarity is a congruence, dynamic bisimilarity coincides with it. In any case it can be characterised as the coarsest bisimulation which is a congruence. Dynamic bisimilarity is a rather stable notion, and can be de ned in several ....

....that a transition system where bisimilarity is not a congruence cannot be represented as a structured coalgebra. Hence, the idea is to modify the system in such a way that bisimilarity in the new system coincides with the coarsest bisimulation which is a congruence in the original system. In [26] such an equivalence has been characterised operationally as dynamic bisimilarity. The basic idea of dynamic bisimulation is to allow at every step of bisimulation not only the execution of an action, but also the embedding of the two agents under measurement within the same, but otherwise ....

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U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171-199, 1992.

....of closure for all contexts . However, this results in a congruence which is no longer a bisimulation (unless bisimilarity was already a congruence) Dynamic bisimulation, instead, performs context closure during the bisimulation game . In particular, dynamic bisimilarity, introduced in [36] to study ccs agents, was shown to capture the coarsest equivalence among weak bisimulations that are also congruences, being completely axiomatized by the axioms of strong observational equivalence plus two of the three Milner s laws. The basic idea is to allow at every step of bisimulation ....

....we have not only that a:nil c a:nil c nil; but also that C[a:nil] c C[ a:nil] c C[nil] Dynamic bisimilarity is the coarsest congruence which is also a bisimulation. Note that context moves are not observed : they are part of the game but not of the lts. Even if not remarked in [36], dynamic bisimulation can however be recasted in ordinary bisimulation over an extended system. Observe that the dynamic extension is an infinitary construction on the lts and is not expressed at the level of the tss, i.e. it remains at the metalevel of specification. Definition 1.7. Given a ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171--196, 1992.

....is explicit, but agents are subject to substitution axioms. It is therefore often necessary to resort to the largest congruence included in the bisimilarity by an operation of closure for all contexts , which results in a congruence which is no longer a bisimulation. Dynamic bisimulation [20], instead, performs such a context closure during the bisimulation game . Dynamic bisimilarity was shown to capture the coarsest equivalence for ccs agents among weak bisimulations that are also congruences, being completely axiomatized by the axioms of strong observational equivalence plus two ....

....a dynamic bisimulation d such that s d t. Thus, w.r.t. Example 1, we have, e.g. nil 6 d :nil. Dynamic bisimilarity is the coarsest congruence which is also a bisimulation. Note that context moves cannot be observed : they are part of the game but not of the lts. Even if not remarked in [20], dynamic bisimulation can however be recasted in ordinary bisimulation over an extended system. Observe that the dynamic extension is an in nitary construction on the lts and is not expressed at the level of the tss, i.e. it remains at the meta level . De nition 5. Given a lts L = T ; ....

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171-196, 1992.

....in terms of Observation equivalence. This exports to the calculus setting existing algorithms and tools for checking process equivalences (e.g. CPS93] Also, by virtue of standard results, the axiomatizations of other forgetting equivalences can be straightforwardly got (e.g. Dynamic [MS92], and Branching [vGW89] both Early and Late) Up to date, the Weak Late calculus bisimulation was only axiomatized relying on the notion of Symbolic bisimulation [Lin95] whose relationship with Branching and Dynamic equivalence is still not investigated. Finally, as during the execution of ....

....instantiation move (this is indeed an easy consequence of a result proved in [FMQ95b] For instance, letting N = fx; zg, the Early tree for the process N : x(y) y = z] 0 (cf. Fig. 1) is displayed in Fig. 2. The calculus also allows to characterize the Branching [vGW89] and the Dynamic [MS92] equivalence, which obviously proliferate into Early and Late N : x(y) P N (y; N (x) P N (y; NewD N ) P N (y; N (z) P N (y; N (z) 0 h N (x) N (x)i uuj j j j j j j j j j j j j j h N (x) N (z)i fflffl h N (x) NewD N i T TT T TT T TT TT T TT ....

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U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI:171--199, 1992.

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Ugo Montanari and Vladimiro Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, XVI:171-199, 1992.

No context found.

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171--196, 1992.

No context found.

U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16(2):171--199, 1992.

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U. Montanari and V. Sassone. Dynamic congruence vs. progressing bisimulation for CCS. Fundamenta Informaticae, 16:171-196, 1992.

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