A. Rabinovich and B. A. Trakhtenbrot. Behaviour structures and nets. Fundamenta Informaticae, 11(4):357--404, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

.... work presented in this thesis are bisimulations for independence (or causality) fairness (or completed observations) and non deterministic dataflow (or explicit I O) Independence bisimulations include pomset bisimulation, historypreserving bisimulation (introduced by Rabinovich and Trakhtenbrot [115], Degano, De Nicola and Montanari [32] and Best, Devillers, Kiehn and Pomello [14] under the name of respectively behaviour structure, mixed ordering and fully concurrent bisimulation) and hereditary historypreserving bisimulation (introduced by Bednarczyk [12] and reappearing from the categorical ....

....bisimulation (HPB) and the hereditary history preserving bisimulation (HHPB) Intuitively, HPB extends the path formulation of bisimulation given in Def. 1.2.2 by requiring that any two related paths must have the same independence structure. As mentioned in Sec. 7. 4, HPB was introduced in [115] and [32] under the name of behaviour structure bisimulation, and mixed ordering (mo) bisimulation respectively. The term history preserving originates from [131] where Goltz and vanGlabbeek define the notion for event structures and prove the key property of HPB, namely that it is preserved ....

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A. Rabinovich and B.A. Trakhtenbrot. Behaviour structures and nets. Fundamenta Informaticae, XI(4):357--404, 1988.

....and captures the abstract notion of concurrent computation, in the sense that all the firing sequences corresponding to linearizations of the partial ordering are considered equivalent. Most semantic and logic notions specifying the concurrent behavior of nets are based on the notion of process [23, 2]. Processes play an important role in the Petri Nets are Monoids approach to net theory [19, 11, 26] In this approach, a net N is analogous to a signature Sigma , and the symmetric monoidal category P(N ) associated to N is analogous to the cartesian category L( Sigma) of terms and ....

A. Rabinovich and B. A. Trakhtenbrot. Behaviour structures and nets. Fundamenta Informaticae, 11:357--404, 1988.

....history preserving bisimulation. Its definition depends on the simple but important remark, that a configuration of an event structure can be regarded as a pomset, with causal dependency relation and labelling got by restricting that of the event structure. Definition: Rabinovitch Trakhtenbrot (Rabinovich and Trakhtenbrot 1988), van Glabeek Goltz (Glabeek and Goltz 1989) A history preserving bisimulation between two event structures E 1 , E 2 consists of a set H of triples (x 1 , f, x 2 ) where x 1 is a configuration of E 1 , x 2 a configuration of E 2 and f is a isomorphism between them (regarded as pomsets) such ....

Rabinovich, A. and B. A. Trakhtenbrot (1988). Behaviour Structure and Nets.

....we consider the two most prominent semantics in this respect. We first show that the usual bisimulation semantics together with a dependency relation on actions indeed gives a causal branching time semantics. It turns out that the induced equivalence is exactly history preserving bisimulation [15, 18]. Then we introduce a version of testing equivalence taking causalities into account (investigated in detail in [5] and show that the corresponding result holds also for testing (or failure) semantics. In order to establish these results, we need a system model which precisely represents ....

.... Semantics We now define two equivalence notions on event structures: The first one is the ordinary strong bisimulation of Park and Milner [13, 11] a pure interleaving equivalence respecting precisely choices between alternative behaviours, and the second one history preserving bisimulation [15, 18] which additionally takes causality into account. 3.1 Definition. Let E ; F be prime event structures. A relation R C(E) Theta C(F) is called a bisimulation between E and F iff ffl ( 2 R and ffl (X; Y ) 2 R implies X Gamma a E X 0 ) 9Y 0 such that Y Gamma a F Y 0 ....

Alexander Rabinovich and B. A. Trakhtenbrot. Behaviour structure and nets. Fundamenta Informaticae, XI(4):357--404, December 1988.

.... because it transforms by coreflections to bisimulations for petri nets, labelled asynchronuos transition systems [NW96] and transition systems with independence [JNW94] It is a strengthening of the history preserving bisimulation (h pb) previously studied by Rabinovitch and Trakhtenbrot [RT88] and van Glabeek and Goltz [VGG89] However, it is still open if hh p bisimulation is decidable for say finite safe nets or finite transition systems with independence, despite the work of a number of people. Even for very limited clases of systems s.t. finite free choice 1safe nets, only ....

A. Rabinovich and B.A. Trakhtenbrot. Behaviour structure and nets. Fundamenta Informaticae, (XI):357--404, 1988.

....models of behaviours by combining models of behaviour components such an equivalence should be a congruence w.r. to the considered operations on configuration structures. There is a number of candidates for such an equivalence. Among them the so called history preserving equivalence (introduced in [7]) seems to be adequate. It can be defined with the aid of a concept of simulation, where a simulation of a configuration structure P in a configuration structure Q is a family ( pq : p 2 P; q 2 Q) of sets of bijective, labels and order preserving correspondences between the respective ....

....can easily be adapted for labelled configuration structures. Some of them are congruences for the considered operations on labelled event structures. We adapt one of such congruences for timed configuration structures. It is a variant of the so called history preserving equivalence (cf. 2] and [7]) As the internal events of timed behaviours have some effect on characteristics of such behaviours, we choose the strongest variant in which internal events are not neglected. Our definition of the history preserving equivalence is based on a concept of simulation. 5.1. Definition. A (history ....

A. RABINOVICH, B. A. TRAKHTENBROT, Behaviour structure and nets, Fundamenta Informaticae 11(4), 1988, pp.357-404

....the possibility of deciding and axiomatizing weak ST bisimulation also when an action refinement operator P [a ; Q] is considered. 1 Introduction Many bisimulation equivalences expressing some form of history dependence have been defined in the literature: history preserving bisimulation [24,10,13], ST bisimulation [12,3,25,16,17,8] and location bisimulation [5,2,22,9] Due to the complex nature of this kind of equivalences it turned out to be not simple to decide (see for instance [18] and, especially, axiomatize them for non trivial classes of systems (e.g. classes which include most ....

A. Rabinovich, B. Trakhtenbrot, "Behaviour Structures and Nets", in Fundamenta Informaticae 11:357-404, 1988.

.... Langerak [49] the families of posets of Rensink [79] and the event automata of Gunawardena [32] and Pinna and Poigne [72] Like most of our models, event structures have been equipped with notions of behavioural equivalences (like the history preserving bisimlation of Rabinovich and Trakhtenbrot [78]) and logics (for some axiomatizations see the works of Mukund, Thiagarajan [58, 59] and Penczek [70] The relationship between event structures and Mazurkiewicz trace languages seems first to have been made explicit by Bednarczyk [5] However, the proof of the representation theorem here appears ....

Rabinovich, A. and Trakhtenbrot, B.A., Behaviour Structure and Nets, Fundamenta Informaticae, XI, 4 pp. 357--404, 1988.

.... end point, presenting somehow the maximum that can be achieved using this particular approach. However, the algebra itself lends itself to further study. For instance, one may try to characterise other, weaker equivalences such as history preserving bisimulation (cf. Rabinovich and Trakhtenbrot [18], Van Glabbeek and Goltz [10] by adding axioms to Ax ; or, regarding our labels A as abstract events rather than actions, one may study the differences between various types of event based models such as (for example) flow or stable event structures (cf. 6, 22] in terms of Ax . 4.2 ....

A. Rabinovich and B. A. Trakhtenbrot. Behaviour structure and nets. Fund. Informaticae, XI(4):357--404, Dec. 1988.

....concurrent runs of nets. From a process, it is possible to derive a partial order of the events of the run, which represents the dependencies between them. A notion of bisimulation, called history preserving bisimulation, which takes into account the partial order behavior has been de ned in [40] for event structures. The same notion has been introduced before in [15] for process calculi, using mixed ordering observations. History preserving bisimulation has been applied to Petri nets in [8] for two nets to simulate, it is required not only that they can perform the same sequence of ....

A. Rabinovich and B. A. Trakhtenbrot. Behaviour structures and nets. Fundamenta Informaticae 11(4):357-404, 1988.

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A. Rabinovich and B. A. Trakhtenbrot. Behaviour structures and nets. Fundamenta Informaticae, 11(4):357--404, 1988.

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Rabinivich, A., Trakhtenbrot, B. A., Behaviour structure and nets, Fundamenta Informaticae 11(4), 1988, 357-404

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