A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357404, 1988.  Home/Search   Document Not in Database   Summary   Related Articles   Check

....bisimulation on labelled event structures. This is only part of the story. The approach yields a notion of bisimulation on a relatively new model of transition systems with independence. Also, the concept of bisimulation induced on labelled event structures is not quite that originally proposed in [10] and [3] but, interestingly, a slight strengthening of the original definition. A logic of path assertions is exhibited it can be viewed as a generalisation of Hennessy Milner logic. Again it is general and applies to many different models, where it is a characteristic logic for the associated ....

....of E it determines a pomset, viz (x; x Theta x) F in(x) x : x L) which we will also call x; here F in(x) consists of all finite subsets of x which coincides with the restriction of Con to subsets of x because configurations are consistent. Definition: Rabinovitch Traktenbrot [10], van Glabeek Goltz [3] 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 that ( 2 H and, ....

Rabinovitch, A., and Traktenbrot, B., Behaviour structures and nets. Fundamenta Informatica, 11(4), pp.357-404, 1988.

.... L or synchronisation trees ST L , L bisimulation coincides with Park and Milner s strong bisimulation; for event structures ES L , Pom L bisimulation coincides with strong history preserving bisimulation due to Bednarczyk refining ideas of van Glabbeek and Goltz, Rabinovitch and Traktenbrot [2, 9, 12]. 5 4 Presheaf models Given a path category P we can build the category b P of presheaves over P . The objects of P consist of functors P Set, to the category of sets. The morphisms of b P are natural transformations between functors. Intuitively a presheaf F : Set can be thought ....

Rabinovitch, A., and Traktenbrot, B., Behaviour structures and nets. Fundamenta Informatica, 11(4), pp.357-404, 1988.

....equivalences. In L , L # bisimulation coincides with Park and Milner s strong bisimulation; for event structures L , Pom L ) bisimulation coincides with hereditary history preserving bisimulation due to Bednarczyk refining ideas of van Glabbeek and Goltz, Rabinovitch and Traktenbrot [1, 12, 26]. The following easy to prove preservation property will be used later. Proposition 1.7 Suppose has products. Let f 1 : M 1 N 1 and f 2 : M 2 N 2 be P open maps. Then f 1 f 2 : M 1 N 1 2 is P open. 1.3 Presheaves as non deterministic processes Presheaf categories are the ....

A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357--404, 1988.

....functors between presheaf categories preserve open maps. For this reason it is possible to prove for presheaf models that open map bisimulation is a congruence with respect to the interpretation of the operators of Proc. We use this result to (re)prove that strong history preserving bisimulation [41, 113] for event structures is a congruence. Further we show that a refinement functor on the particular presheaf model that extends event structures obtained as a colimit preserving functor coincides on event structures with a refinement proposed in [41] and again this entails that such a strong ....

....obtain known equivalences. In L , L # bisimulation coincides with Park and Milner s strong bisimulation; for event structures L , PomL bisimulation coincides with strong history preserving bisimulation due to Bednarczyk refining ideas of van Glabbeek and Goltz, Rabinovitch and Traktenbrot [8, 41, 113]. Theorem 2.2.5 (Theorem 2 and Theorem 10(i) of [64] Two transition systems (and so synchronisation trees) over the labelling set L are L # bisimilar i# they are strongly bisimilar in the sense of [82] Two event structures with labelling sets L are PomL open bisimilar if and only if they ....

A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357--404, 1988.

.... paths, the definition agrees with the strong bisimulation of Milner [12] and in the case of event structures with nonsequential paths in the form of pomsets, the definition yielded an interesting strengthening of the history preserving bisimulation introduced by Rabinovitch and Trakhtenbrot [20]. Here we show how the coreflection from other models to nets combined with abstract properties of the general definition of bisimulation from [8] provides a notion of bisimulation on nets which automatically inherits a number of important properties. The main message of this paper is that the ....

....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 [20], van Glabeek Goltz [6] 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 that ( 2 H and, ....

Rabinovitch, A., and Trakhtenbrot, B., Behaviour structures and nets. Fundamenta Informatica, 11(4), pp. 357--404, 1988.

.... De ne po( ID = h[n] E ID ; l i, where n and l are obtained as above, while E ID is the transitive closure of ID which is de ned as i ID j if i j and either not e i Ie j or j is A i dependent on i , where s i = A i ; s i ) 23 History preserving bisimulation [46, 23, 17] is a bisimulation between runs of processes which accounts for causality by requiring related runs to originate isomorphic partial orders of transitions: De nition 5.4 If T is an N LATS, de ne Run(T ) to be the set of runs of T . If is a run I i 1 e1 s 1 2 e2 s 2 n ....

A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357-404, 1988.

.... De ne po(r) ID = h[n] E r ID ; l r i, where n and l r are obtained as above, while E r ID is the transitive closure of r ID which is de ned as i r ID j if i j and either : e i Ie j ) or j is A i dependent on i , where s i = A i ; s i ) History preserving bisimulation [RT88, GG89, DDNM88b] is a bisimulation between runs of processes which accounts for causality by requiring related runs to originate isomorphic partial orders of transitions: De nition 6.4 Let T 1 and T 2 be two N LATSs with initial name set I and let Run(T i ) for i = 1; 2) be the corresponding sets of runs. A ....

A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357404, 1988.

....bisimulation on labelled event structures. This is only part of the story. The approach yields a notion of bisimulation on a relatively new model of transition systems with independence. Also, the concept of bisimulation induced on labelled event structures is not quite that originally proposed in [8] and [3] but, interestingly, a slight strengthening of the original definition. A logic of path assertions is exhibited it can be viewed as a generalisation of Hennessy Milner logic. Again it is general and applies to many different models, where it is a characteristic logic for the associated ....

.... are BranL bisimilar iff they are strongly bisimilar in the sense of [7] In the case of event structures taking the path objects P to be pomsets yields a reasonable strengthening of a previously studied equivalence, that of historypreserving bisimulation: Definition: Rabinovitch Traktenbrot [8], van Glabeek Goltz [3] 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 that ( 2 H and, ....

Rabinovitch, A., and Traktenbrot, B., Behaviour structures and nets. Fundamenta Informatica, 11(4), pp.357-404, 1988.

.... TSL or synchronisation trees STL , L bisimulation coincides with Park and Milner s strong bisimulation; for event structures ESL , PomL bisimulation coincides with strong history preserving bisimulation due to Bednarczyk refining ideas of van Glabbeek and Goltz, Rabinovitch and Traktenbrot [2,9,14]. 4 Presheaf Models Let P be a path category. The category of presheaves over P , often denoted by b P or by Set P op , is the category whose objects are contravariant functors from P to Set (the category of sets and functions) and whose arrows are the natural transformations between such ....

Rabinovitch, A., and Traktenbrot, B., Behaviour structures and nets. Fundamenta Informatica, 11(4), pp.357-404, 1988.

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A. Rabinovitch and B. Traktenbrot. Behaviour structures and nets. Fundamenta Informatica, 11(4):357404, 1988.

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