M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps (extended abstract). In Proceedings of LICS'99, pages 6776. IEEE, 1999. 11  Home/Search   Document Details and Download   Summary   Related Articles   Check

....hand, one may ask whether conciseness leads to useful subcategories in their setting. Does conciseness yield interesting constructions if we take our morphisms to be (generalizations of) functional simulations, as in ibid On the other hand, does the further consideration of weak bisimulations in [9] shed light on remaining work in our setting 7 Acknowledgments We thank Jan Willem Klop, whose ideas initiated this exercise, for many useful discussions. We also thank Frits Vaandrager for reading a draft of this paper and providing valuable suggestions. The definition of obviously concise ....

Fiore, M.P., Cattani, G.L., Winskel, G.: Weak bisimulation and open maps. In: Logic in Computer Science. (1999) 67--76

....to unify models of concurrency and their notions of bisimulation into one framework, a domain theory based on presheaf models and open map bisimulation. The endeavor was initiated by Joyal, Nielsen and Winskel in [15] and pursued further in two PhD theses [3, 11] and a number of papers including [6, 20, 5, 4, 13, 21, 9, 12, 7]. Presheaf models are instantiations of the following situation: Let P be a small category in which objects are viewed as computation path shapes with morphisms saying how paths can be extended. The path category P embeds via Yoneda in the category = P , Set] of presheaves over P in which ....

Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps (extended abstract). In LICS'99, Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, pages 67--76. IEEE Computer Society Press, 1999.

....definitions and standard examples. The paper [71] also suggested a class of abstract models for concurrency, the presheaf models for concurrency, which came with a canonical notion of bisimulation from open maps. The general theory of presheaf models have been developed over the last 5 years [71, 22, 143, 147, 21, 144, 19, 24, 37], culminating in the recent thesis of Cattani. We summarise some of the most important results in Sec. 2.3. 2.1 Models for Concurrency The work reported in the chapter [146] was initiated by work of Winskel [140] followed by work of Nielsen, Rozenberg and Thiagarajan [99] and Sassone et al. ....

....categories and connected colimit preserving functors, which seems like a natural setting in which to study typed concurrency. The dataflow semantics presented in Ch. 8 is given in a subcategory of the category of connected colimit preserving functors. Further work. Recently it has been shown in [37] how the notion of weak bisimulation can be described abstractly in presheaf models, exploiting the view of presheaf categories as discrete fibrations. In the case of synchronisation trees Milner s observational congruence appears naturally from the abstract definition. For the more expressive ....

Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, 1999.

....the dynamics involved in the simulation. The realisability aspect remains informal throughout, a sequel of this paper will make the connection precise. 1 Introduction Since many years by now there has been a continuing interest in abstract characterisations of bisimulation (cf. Winskel et.al. [9, 6]) and the main technical development of this paper proceeds along those lines. We study in further detail issues originally considered by Claudio Hermida (cf. 7] culminating in a characterisation of simulation in terms of modules. The latter notion is geared towards 1 computer science and ....

Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science. IEEE Computer Society Press, 1999.

....be a core ective subcategory of the category of transition systems suited for operational semantics. Another force was added by the notion of bisimulation from open maps introduced in [9] Here one gets an abstract behavioural equivalence by choosing a path category , or to be a bit more general [14], a functor from a category of path shapes to the model at issue, identifying the observable computations (in [9] assumed to be the inclusion of a subcategory) The open maps approach gained ground through the further development [10,11,15,13,16] of the presheaf models for concurrency also ....

M. Fiore, G. L. Cattani, G. Winskel, Weak bisimulation and open maps, in: Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, 1999, pp. 67-76.

....category of sets of labels; co fibration model substitution, or relabelling, and fibrations model inverse relabelling and restriction. Furthermore, because a category P is embedded in the presheaf category P, the presheaf category comes with a notion of bisimulation [JNW96] and weak bisimulation [FCW99]. Presheaf models have been given to CCS like languages [CW96] a value passing version of CCS [Win96] and the p calculus [CSW97] An approach towards a theory of domains for concurrency based on presheaf models is presented in [CFW98] Presheaf models differ from the models presented before in ....

Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps. In Proc. LICS, 1999.

....be a coreflective subcategory of the category of transition systems suited for operational semantics. Another force was added by the notion of bisimulation from open maps introduced in [19] Here one gets an abstract behavioural equivalence by choosing a path category, or to be a bit more general [12], a functor from a category of path shapes to the model at issue, identifying the observable computations (in [19] assumed to be the inclusion of a subcategory) The open maps approach gained ground through the further development [4, 7, 6, 29, 4, 8] of the presheaf models for concurrency also ....

M. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, 1999.

.... the ideas of Pitts [Pit96] but rather than using Tarski s theorem, we give an abstract version of the treatment of predicates in [SP82] We take a fibrational approach following Hermida [Her93] Hermida and Jacobs [HJ98] and what we do is essentially a special case of Fiore, Cattani and Winskel [FCW99]. So let us begin with a category K and a functor P : K op # Pos (the category of partial orders) We think of elements P of P(x) as predicates over x and of P(f)Q as f 1 (Q) we write f # (Q) for P(f)Q. We can form the total category K t with objects of the form x, P (where P # ....

M. P. Fiore, G. L. Cattani and G. Winskel, Weak Bisimulation and Open Maps, in Proc. 14th LICS, pp. 67--76, Washington: IEEE Computer Society Press, 1999.

....category of sets of labels; co fibration model substitution, or relabelling, and fibrations model inverse relabelling and restriction. Furthermore, because a category P is embedded in the presheaf category P, the presheaf category comes with a notion of bisimulation [JNW96] and weak bisimulation [FCW99]. Presheaf models have been given to CCS like languages [CW96] a value passing version of CCS [Win96] and the p calculus [CSW97] An approach towards a theory of domains for concurrency based on presheaf models is presented in [CFW98] Presheaf models differ from the models presented before in ....

Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps. In Proc. LICS, 1999.

....depending only on properties of the pre xed sum, so that it holds also for other choices of exponential. The language has no distinguished invisible action , so there is the issue of how to support more abstract operational equivalences such as weak bisimulation, perhaps starting from [5]. Work is in progress on extending the idea of pre xed sum to include namegeneration as in Milner s calculus. The calculus already has a presheaf semantics [6] but it has not been extended to higher order (see [22] for an operational extension) We hope to be able to link up with the work on ....

G. L. Cattani, M. Fiore, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99.

....then transfer these preservation properties to concrete models like synchronisation trees and event structures, through canonical embeddings using results such as Proposition 5.5. Working with presheaves also avoids some obstructions to a treatment of weak bisimulation on independence models [10], though this topic is not dealt with here. A more general, and probably the most important, motivation for presheaf models is the hope they give of making concurrency less separate a study. Through presheaf models we are trying to bring concurrency theory within domain theory, though with the ....

.... advantage of the preservation properties of universal constructions a strategy proposed in the conclusion of [19] to the constructions of presheaf models for more sophisticated languages [5, 3] Other applications, to nondeterministic dataflow, fairness and weak bisimulation, can be found in [16, 15, 10]. Specifically, this paper builds on the analysis of the handbook chapter [29] with open map bisimulation in mind, to axiomatise a presheaf based semantics of the general purpose process language Proc treated there. On top of the categorical structure which is needed for the semantics of Proc, ....

M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps (extended abstract). In LICS '99, Proceedings of the Fourteenth Annual IEEE Symposium on Logic in Computer Science, pages 67--76. IEEE Computer Society Press, 1999.

.... new names are communicated (though this can also be done domain theoretically) Secondly, it supports a direct de nition of weak bisimulation, something the domain model lacks completely and the presheaf model can, as far as we know, only achieve indirectly by means of a saturation construction [19]. It is also worth noticing that while the domain models are tailored for late bisimulation, our focus here is on early semantics, both to obtain a simpler notion of transition system, and because we have found the early style suits work on concurrent language semantics and on secure ....

M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps (extended abstract). In LICS '99 [34], pages 67-76. 40

.... in which only new names are communicated (though this can also be done domain theoretically) Secondly, it supports a direct de nition of weak bisimulation, something the domain model lacks and the presheaf model can, as far as we know, only achieve indirectly by means of a saturation construction [FCW99]. It is also worth noticing that while the domain models are tailored for late bisimulation, our focus here is on early semantics, both to obtain a simpler notion of transition system, and because we have found the early style suits work on concurrent language semantics and on secure ....

M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps (extended abstract). In Proceedings of LICS'99, pages 6776. IEEE, 1999. 11

....using presheaves and profunctors to model process calculi, and we suggest directions for future research. We do not address weak bisimulation at all here. In no way do we suggest that it is unimportant. But it is a large issue and the ideas of how to extend weak bisimulation to presheaf models [12] are still fresh. We expect that our axiomatics may allow a similar development, but we are not sure yet. It is not clear to us whether directly modelling weak bisimulation is the most interesting development. It may be better to develop a notion of contextual equivalence, using strong ....

M. Fiore, G. L. Cattani and G. Winskel. Weak bisimulation and open maps. Manuscript, 1998.

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M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps (extended abstract). In Proceedings of LICS'99, pages 6776. IEEE, 1999. 11

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Fiore, M.P., Cattani, G.L., Winskel, G.: Weak bisimulation and open maps. In: Logic in Computer Science. (1999) 67--76

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M. Fiore, G.L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99, pages 67--76. IEEE, 1999.

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M. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99.

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M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99.

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M. P. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99.

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M. Fiore, G. L. Cattani, and G. Winskel. Weak bisimulation and open maps. In Proc. LICS'99.

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Marcelo Fiore, Gian Luca Cattani, and Glynn Winskel. Weak bisimulation and open maps. In Proc. LICS, 1999.

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